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Simplifying (20 + -2x)(20 + -2x)(x) = 0 Reorder the terms for easier multiplication: x(20 + -2x)(20 + -2x) = 0 Multiply (20 + -2x) * (20 + -2x) x(20(20 + -2x) + -2x * (20 + -2x)) = 0 x((20 * 20 + -2x * 20) + -2x * (20 + -2x)) = 0 x((400 + -40x) + -2x * (20 + -2x)) = 0 x(400 + -40x + (20 * -2x + -2x * -2x)) = 0 x(400 + -40x + (-40x + 4x2)) = 0 Combine like terms: -40x + -40x = -80x x(400 + -80x + 4x2) = 0 (400 * x + -80x * x + 4x2 * x) = 0 (400x + -80x2 + 4x3) = 0 Solving 400x + -80x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(100 + -20x + x2) = 0 Factor a trinomial. 4x((10 + -1x)(10 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Subproblem 3
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {0, 10, 10}
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