Find the value of \( x \) in the equation \( 3x^2 - 12x + 9 = 0 \).

["# How to Find the Value of ( x ) in the Equation ( 3x^2 - 12x + 9 = 0 ) – A Step-by-Step Guide", "Solving quadratic equations is a fundamental skill in algebra, and finding the value(s) of ( x ) in equations like ( 3x^2 - 12x + 9 = 0 ) is an essential concept. Whether you're a high school student, a self-learner, or a teacher explaining the topic, understanding how to solve this equation step-by-step can greatly improve your problem-solving skills. In this article, we’ll walk you through finding the value(s) of ( x ) in the equation ( 3x^2 - 12x + 9 = 0 ) and highlight key algebraic techniques along the way.", "---", "## Understanding the Equation", "We begin with the standard quadratic form:", "[\n3x^2 - 12x + 9 = 0\n]", "Quadratic equations take the form ( ax^2 + bx + c = 0 ), where ( a <br/>\neq 0 ). Here, ( a = 3 ), ( b = -12 ), and ( c = 9 ). Solving for ( x ) involves determining the roots of the equation, which represent the values where the parabola intersects the x-axis.", "---", "## Step 1: Simplify the Equation (Factor Out the Greatest Common Factor)", "Before applying formulas, check if the equation can be simplified. The coefficients 3, -12, and 9 share a common factor of 3. Factoring it out gives:", "[\n3(x^2 - 4x + 3) = 0\n]", "Divide both sides by 3:", "[\nx^2 - 4x + 3 = 0\n]", "Now we solve the simplified quadratic equation ( x^2 - 4x + 3 = 0 ).", "---", "## Step 2: Factor the Quadratic Expression", "We now focus on factoring ( x^2 - 4x + 3 ). We seek two numbers that multiply to ( +3 ) and add to ( -4 ).", "These numbers are ( -1 ) and ( -3 ), because:", "[\n(-1) \ imes (-3) = 3 \quad \ ext{and} \quad (-1) + (-3) = -4\n]", "Therefore, we can factor the quadratic as:", "[\n(x - 1)(x - 3) = 0\n]", "---", "## Step 3: Apply the Zero Product Property", "The zero product property states that if a product of factors is zero, then at least one factor must be zero. So, set each factor equal to zero:", "[\nx - 1 = 0 \quad \ ext{or} \quad x - 3 = 0\n]", "Solving these gives:", "[\nx = 1 \quad \ ext{or} \quad x = 3\n]", "---", "## Final Answer", "The values of ( x ) that satisfy the equation ( 3x^2 - 12x + 9 = 0 ) are:", "[\n\boxed{x = 1} \quad \ ext{and} \quad \boxed{x = 3}\n]", "---", "## Why This Method Works", "Factoring is one of the most straightforward methods for solving quadratics when the equation is factorable—as seen here. It leverages algebraic structure to break the problem into simpler, solvable components. While not all quadratics factor neatly, when they do, this method efficiently provides exact real solutions.", "---", "## Additional Insight: Using the Quadratic Formula", "For equations that resist factoring, the quadratic formula provides a universal solution:", "[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "For our simplified equation ( x^2 - 4x + 3 = 0 ), with ( a = 1 ), ( b = -4 ), ( c = 3 ), the discriminant is:", "[\n\Delta = (-4)^2 - 4(1)(3) = 16 - 12 = 4\n]", "Thus,", "[\nx = \frac{4 \pm \sqrt{4}}{2} = \frac{4 \pm 2}{2}\n]", "This yields:", "[\nx = \frac{6}{2} = 3 \quad \ ext{and} \quad x = \frac{2}{2} = 1\n]", "Confirming our earlier results.", "---", "## Summary", "- Factoring simplifies solving quadratic equations when possible.\n- The zero product property helps isolate variable solutions.\n- Always verify using the quadratic formula for accuracy.\n- Understanding these techniques builds a strong foundation in algebra and prepares you for more advanced topics.", "If you’re looking to solve equations like ( 3x^2 - 12x + 9 = 0 ), remember to simplify first, factor carefully, and apply fundamental algebraic rules. Mastering these steps leads to confidence in tackling quadratic equations.", "---", "Keywords: find value of x, solve 3x² – 12x + 9 = 0, quadratic equation, algebra, factoring quadratics, zero product property, quadratic formula, algebraic solutions, equation steps.", "---", "Start today by practicing this equation—and soon, solving quadratics will feel second nature!"]