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Simplifying 12x3 = 8x + -10x2 Solving 12x3 = 8x + -10x2 Solving for variable 'x'. Reorder the terms: -8x + 10x2 + 12x3 = 8x + -10x2 + -8x + 10x2 Reorder the terms: -8x + 10x2 + 12x3 = 8x + -8x + -10x2 + 10x2 Combine like terms: 8x + -8x = 0 -8x + 10x2 + 12x3 = 0 + -10x2 + 10x2 -8x + 10x2 + 12x3 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 -8x + 10x2 + 12x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(-4 + 5x + 6x2) = 0 Factor a trinomial. 2x((-4 + -3x)(1 + -2x)) = 0 Ignore the factor 2.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 '(-4 + -3x)' equal to zero and attempt to solve: Simplifying -4 + -3x = 0 Solving -4 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -3x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3x = 0 + 4 -3x = 0 + 4 Combine like terms: 0 + 4 = 4 -3x = 4 Divide each side by '-3'. x = -1.333333333 Simplifying x = -1.333333333Subproblem 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, -1.333333333, 0.5}
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