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Simplifying x(3x + -2)(x + 6) = 0 Reorder the terms: x(-2 + 3x)(x + 6) = 0 Reorder the terms: x(-2 + 3x)(6 + x) = 0 Multiply (-2 + 3x) * (6 + x) x(-2(6 + x) + 3x * (6 + x)) = 0 x((6 * -2 + x * -2) + 3x * (6 + x)) = 0 x((-12 + -2x) + 3x * (6 + x)) = 0 x(-12 + -2x + (6 * 3x + x * 3x)) = 0 x(-12 + -2x + (18x + 3x2)) = 0 Combine like terms: -2x + 18x = 16x x(-12 + 16x + 3x2) = 0 (-12 * x + 16x * x + 3x2 * x) = 0 (-12x + 16x2 + 3x3) = 0 Solving -12x + 16x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-12 + 16x + 3x2) = 0 Factor a trinomial. x((-6 + -1x)(2 + -3x)) = 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 '(-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 = -6Subproblem 3
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {0, -6, 0.6666666667}
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