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