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Simplifying (10 + -2x)(6 + -2x)(x) = 0 Reorder the terms for easier multiplication: x(10 + -2x)(6 + -2x) = 0 Multiply (10 + -2x) * (6 + -2x) x(10(6 + -2x) + -2x * (6 + -2x)) = 0 x((6 * 10 + -2x * 10) + -2x * (6 + -2x)) = 0 x((60 + -20x) + -2x * (6 + -2x)) = 0 x(60 + -20x + (6 * -2x + -2x * -2x)) = 0 x(60 + -20x + (-12x + 4x2)) = 0 Combine like terms: -20x + -12x = -32x x(60 + -32x + 4x2) = 0 (60 * x + -32x * x + 4x2 * x) = 0 (60x + -32x2 + 4x3) = 0 Solving 60x + -32x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(15 + -8x + x2) = 0 Factor a trinomial. 4x((3 + -1x)(5 + -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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {0, 3, 5}
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