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Simplifying (3x3 + -18x2)(-2x + 12) = 0 Reorder the terms: (-18x2 + 3x3)(-2x + 12) = 0 Reorder the terms: (-18x2 + 3x3)(12 + -2x) = 0 Multiply (-18x2 + 3x3) * (12 + -2x) (-18x2 * (12 + -2x) + 3x3 * (12 + -2x)) = 0 ((12 * -18x2 + -2x * -18x2) + 3x3 * (12 + -2x)) = 0 ((-216x2 + 36x3) + 3x3 * (12 + -2x)) = 0 (-216x2 + 36x3 + (12 * 3x3 + -2x * 3x3)) = 0 (-216x2 + 36x3 + (36x3 + -6x4)) = 0 Combine like terms: 36x3 + 36x3 = 72x3 (-216x2 + 72x3 + -6x4) = 0 Solving -216x2 + 72x3 + -6x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x2'. 6x2(-36 + 12x + -1x2) = 0 Factor a trinomial. 6x2((-6 + x)(6 + -1x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 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 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Subproblem 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, 6, 6}
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