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Simplifying 27x(x + 2) = 3240 Reorder the terms: 27x(2 + x) = 3240 (2 * 27x + x * 27x) = 3240 (54x + 27x2) = 3240 Solving 54x + 27x2 = 3240 Solving for variable 'x'. Reorder the terms: -3240 + 54x + 27x2 = 3240 + -3240 Combine like terms: 3240 + -3240 = 0 -3240 + 54x + 27x2 = 0 Factor out the Greatest Common Factor (GCF), '27'. 27(-120 + 2x + x2) = 0 Factor a trinomial. 27((-12 + -1x)(10 + -1x)) = 0 Ignore the factor 27.Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve: Simplifying -12 + -1x = 0 Solving -12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1x = 0 + 12 -1x = 0 + 12 Combine like terms: 0 + 12 = 12 -1x = 12 Divide each side by '-1'. x = -12 Simplifying x = -12Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {-12, 10}
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