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Simplifying 6x(12 + -4x)(5 + 15x) = 0 Multiply (12 + -4x) * (5 + 15x) 6x(12(5 + 15x) + -4x * (5 + 15x)) = 0 6x((5 * 12 + 15x * 12) + -4x * (5 + 15x)) = 0 6x((60 + 180x) + -4x * (5 + 15x)) = 0 6x(60 + 180x + (5 * -4x + 15x * -4x)) = 0 6x(60 + 180x + (-20x + -60x2)) = 0 Combine like terms: 180x + -20x = 160x 6x(60 + 160x + -60x2) = 0 (60 * 6x + 160x * 6x + -60x2 * 6x) = 0 (360x + 960x2 + -360x3) = 0 Solving 360x + 960x2 + -360x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '120x'. 120x(3 + 8x + -3x2) = 0 Factor a trinomial. 120x((3 + -1x)(1 + 3x)) = 0 Ignore the factor 120.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 '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {0, 3, -0.3333333333}
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