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Simplifying 0 = 9x2 + 24x + 12 Reorder the terms: 0 = 12 + 24x + 9x2 Solving 0 = 12 + 24x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -12 = -12 -12 + -24x + -9x2 = 12 + 24x + 9x2 + -12 + -24x + -9x2 Reorder the terms: -12 + -24x + -9x2 = 12 + -12 + 24x + -24x + 9x2 + -9x2 Combine like terms: 12 + -12 = 0 -12 + -24x + -9x2 = 0 + 24x + -24x + 9x2 + -9x2 -12 + -24x + -9x2 = 24x + -24x + 9x2 + -9x2 Combine like terms: 24x + -24x = 0 -12 + -24x + -9x2 = 0 + 9x2 + -9x2 -12 + -24x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -12 + -24x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(4 + 8x + 3x2) = 0 Factor a trinomial. -3((2 + x)(2 + 3x)) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 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 = -0.6666666667Solution
x = {-2, -0.6666666667}
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