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Simplifying x(x + -5)(2x + -6) = 0 Reorder the terms: x(-5 + x)(2x + -6) = 0 Reorder the terms: x(-5 + x)(-6 + 2x) = 0 Multiply (-5 + x) * (-6 + 2x) x(-5(-6 + 2x) + x(-6 + 2x)) = 0 x((-6 * -5 + 2x * -5) + x(-6 + 2x)) = 0 x((30 + -10x) + x(-6 + 2x)) = 0 x(30 + -10x + (-6 * x + 2x * x)) = 0 x(30 + -10x + (-6x + 2x2)) = 0 Combine like terms: -10x + -6x = -16x x(30 + -16x + 2x2) = 0 (30 * x + -16x * x + 2x2 * x) = 0 (30x + -16x2 + 2x3) = 0 Solving 30x + -16x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(15 + -8x + x2) = 0 Factor a trinomial. 2x((3 + -1x)(5 + -1x)) = 0 Ignore the factor 2.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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