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