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Simplifying 12x2 = 27x + -6 Reorder the terms: 12x2 = -6 + 27x Solving 12x2 = -6 + 27x Solving for variable 'x'. Reorder the terms: 6 + -27x + 12x2 = -6 + 27x + 6 + -27x Reorder the terms: 6 + -27x + 12x2 = -6 + 6 + 27x + -27x Combine like terms: -6 + 6 = 0 6 + -27x + 12x2 = 0 + 27x + -27x 6 + -27x + 12x2 = 27x + -27x Combine like terms: 27x + -27x = 0 6 + -27x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(2 + -9x + 4x2) = 0 Factor a trinomial. 3((1 + -4x)(2 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Subproblem 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 = {0.25, 2}
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