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Simplifying x(x + 12)(x + -6) = 0 Reorder the terms: x(12 + x)(x + -6) = 0 Reorder the terms: x(12 + x)(-6 + x) = 0 Multiply (12 + x) * (-6 + x) x(12(-6 + x) + x(-6 + x)) = 0 x((-6 * 12 + x * 12) + x(-6 + x)) = 0 x((-72 + 12x) + x(-6 + x)) = 0 x(-72 + 12x + (-6 * x + x * x)) = 0 x(-72 + 12x + (-6x + x2)) = 0 Combine like terms: 12x + -6x = 6x x(-72 + 6x + x2) = 0 (-72 * x + 6x * x + x2 * x) = 0 (-72x + 6x2 + x3) = 0 Solving -72x + 6x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-72 + 6x + x2) = 0 Factor a trinomial. x((-12 + -1x)(6 + -1x)) = 0Subproblem 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 '(-12 + -1x)' equal to zero and attempt to solve: Simplifying -12 + -1x = 0 Solving -12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1x = 0 + 12 -1x = 0 + 12 Combine like terms: 0 + 12 = 12 -1x = 12 Divide each side by '-1'. x = -12 Simplifying x = -12Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {0, -12, 6}
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