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Simplifying 6x2 + 12 = 27x Reorder the terms: 12 + 6x2 = 27x Solving 12 + 6x2 = 27x Solving for variable 'x'. Reorder the terms: 12 + -27x + 6x2 = 27x + -27x Combine like terms: 27x + -27x = 0 12 + -27x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -9x + 2x2) = 0 Factor a trinomial. 3((1 + -2x)(4 + -1x)) = 0 Ignore the factor 3.Subproblem 1
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 = 0.5Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {0.5, 4}
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