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Simplifying 9x(2 + 3x)(-2 + -3x) = 0 Multiply (2 + 3x) * (-2 + -3x) 9x(2(-2 + -3x) + 3x * (-2 + -3x)) = 0 9x((-2 * 2 + -3x * 2) + 3x * (-2 + -3x)) = 0 9x((-4 + -6x) + 3x * (-2 + -3x)) = 0 9x(-4 + -6x + (-2 * 3x + -3x * 3x)) = 0 9x(-4 + -6x + (-6x + -9x2)) = 0 Combine like terms: -6x + -6x = -12x 9x(-4 + -12x + -9x2) = 0 (-4 * 9x + -12x * 9x + -9x2 * 9x) = 0 (-36x + -108x2 + -81x3) = 0 Solving -36x + -108x2 + -81x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-9x'. -9x(4 + 12x + 9x2) = 0 Factor a trinomial. -9x((2 + 3x)(2 + 3x)) = 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 '(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 = -0.6666666667Subproblem 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, -0.6666666667, -0.6666666667}
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