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Simplifying 5x(2x + -12)(3x + 15) = 0 Reorder the terms: 5x(-12 + 2x)(3x + 15) = 0 Reorder the terms: 5x(-12 + 2x)(15 + 3x) = 0 Multiply (-12 + 2x) * (15 + 3x) 5x(-12(15 + 3x) + 2x * (15 + 3x)) = 0 5x((15 * -12 + 3x * -12) + 2x * (15 + 3x)) = 0 5x((-180 + -36x) + 2x * (15 + 3x)) = 0 5x(-180 + -36x + (15 * 2x + 3x * 2x)) = 0 5x(-180 + -36x + (30x + 6x2)) = 0 Combine like terms: -36x + 30x = -6x 5x(-180 + -6x + 6x2) = 0 (-180 * 5x + -6x * 5x + 6x2 * 5x) = 0 (-900x + -30x2 + 30x3) = 0 Solving -900x + -30x2 + 30x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '30x'. 30x(-30 + -1x + x2) = 0 Factor a trinomial. 30x((-5 + -1x)(6 + -1x)) = 0 Ignore the factor 30.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 '(-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 = -5Subproblem 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, -5, 6}
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