Equation: (20-2x)(15-2x)=240 → 300 -40x -30x +4x²=240 → 4x² -70x +60=0 → 2x² -35x +30=0.

["Solving the Quadratic Equation: (20−2x)(15−2x)=240", "When faced with a quadratic equation, understanding the step-by-step process to solve it can greatly simplify the task. One such equation is:", "[\n(20 - 2x)(15 - 2x) = 240\n]", "This expression represents a product of two linear binomials set equal to a constant, which expands into a standard quadratic form. Let’s walk through the full solution.", "---", "### Step 1: Expand the Left-Hand Side", "Start by expanding the product on the left-hand side:", "[\n(20 - 2x)(15 - 2x) = 20 \cdot 15 + 20 \cdot (-2x) + (-2x) \cdot 15 + (-2x)(-2x)\n]", "Calculating each term:", "- (20 \cdot 15 = 300)\n- (20 \cdot (-2x) = -40x)\n- ((-2x) \cdot 15 = -30x)\n- ((-2x)(-2x) = 4x^2)", "Add them together:", "[\n300 - 40x - 30x + 4x^2 = 4x^2 - 70x + 300\n]", "So the equation becomes:", "[\n4x^2 - 70x + 300 = 240\n]", "---", "### Step 2: Bring All Terms to One Side", "Subtract 240 from both sides to form a standard quadratic equation:", "[\n4x^2 - 70x + 300 - 240 = 0\n]", "[\n4x^2 - 70x + 60 = 0\n]", "---", "### Step 3: Simplify the Equation", "Divide all terms by 2 to reduce the coefficients:", "[\n2x^2 - 35x + 30 = 0\n]", "This simplified equation is often easier to work with and solve.", "---", "### Step 4: Solve the Quadratic Using the Quadratic Formula", "The standard form is (ax^2 + bx + c = 0), where:", "- (a = 2)\n- (b = -35)\n- (c = 30)", "The quadratic formula is:", "[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "Compute the discriminant:", "[\nb^2 - 4ac = (-35)^2 - 4(2)(30) = 1225 - 240 = 985\n]", "Since the discriminant is positive, there are two real solutions.", "Now compute the roots:", "[\nx = \frac{35 \pm \sqrt{985}}{4}\n]", "---", "### Step 5: Approximate the Solutions", "Because √985 is irrational (approximately 31.38), the solutions are approximately:", "[\nx = \frac{35 + 31.38}{4} \approx \frac{66.38}{4} \approx 16.60\n]", "[\nx = \frac{35 - 31.38}{4} \approx \frac{3.62}{4} \approx 0.905\n]", "These values can be verified by plugging back into the original equation.", "---", "### Summary", "- Original equation: ((20 - 2x)(15 - 2x) = 240)\n- Expanded form: (4x^2 - 70x + 300 = 240)\n- Simplified quadratic: (2x^2 - 35x + 30 = 0)\n- Solutions using quadratic formula:", "[\n\boxed{x = \frac{35 \pm \sqrt{985}}{4}}\n]", "This structured approach is essential in algebra for solving and understanding quadratic equations arising from expanded products. If you're learning algebra or tackling similar problems, practicing expansion and simplification ensures a solid foundation for solving quadratic equations efficiently.", "---", "### Key Takeaways:", "- Expand products carefully before forming the quadratic equation.\n- Always simplify coefficients when possible.\n- Use the quadratic formula for accurate real solutions.\n- Verifying results by substitution strengthens problem-solving confidence.", "---", "Keywords: quadratic equation, solve (20−2x)(15−2x)=240, expand and simplify, quadratic formula, 2x²−35x+30=0, algebra solution, equation solving steps", "---", "Understanding how this equation transforms from a factored product into a solvable quadratic not only solves the problem but also builds critical algebraic insight."]