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Simplifying 4x(x + 3)(x + -6) = 0 Reorder the terms: 4x(3 + x)(x + -6) = 0 Reorder the terms: 4x(3 + x)(-6 + x) = 0 Multiply (3 + x) * (-6 + x) 4x(3(-6 + x) + x(-6 + x)) = 0 4x((-6 * 3 + x * 3) + x(-6 + x)) = 0 4x((-18 + 3x) + x(-6 + x)) = 0 4x(-18 + 3x + (-6 * x + x * x)) = 0 4x(-18 + 3x + (-6x + x2)) = 0 Combine like terms: 3x + -6x = -3x 4x(-18 + -3x + x2) = 0 (-18 * 4x + -3x * 4x + x2 * 4x) = 0 (-72x + -12x2 + 4x3) = 0 Solving -72x + -12x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-18 + -3x + x2) = 0 Factor a trinomial. 4x((-3 + -1x)(6 + -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 '(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, -3, 6}
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