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