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Simplifying -9x(x + -6)(2x + 1) = 0 Reorder the terms: -9x(-6 + x)(2x + 1) = 0 Reorder the terms: -9x(-6 + x)(1 + 2x) = 0 Multiply (-6 + x) * (1 + 2x) -9x(-6(1 + 2x) + x(1 + 2x)) = 0 -9x((1 * -6 + 2x * -6) + x(1 + 2x)) = 0 -9x((-6 + -12x) + x(1 + 2x)) = 0 -9x(-6 + -12x + (1 * x + 2x * x)) = 0 -9x(-6 + -12x + (1x + 2x2)) = 0 Combine like terms: -12x + 1x = -11x -9x(-6 + -11x + 2x2) = 0 (-6 * -9x + -11x * -9x + 2x2 * -9x) = 0 (54x + 99x2 + -18x3) = 0 Solving 54x + 99x2 + -18x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9x'. 9x(6 + 11x + -2x2) = 0 Factor a trinomial. 9x((6 + -1x)(1 + 2x)) = 0 Ignore the factor 9.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 '(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 '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {0, 6, -0.5}
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