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Simplifying (12 + 2x)(x) = 630 Reorder the terms for easier multiplication: x(12 + 2x) = 630 (12 * x + 2x * x) = 630 (12x + 2x2) = 630 Solving 12x + 2x2 = 630 Solving for variable 'x'. Reorder the terms: -630 + 12x + 2x2 = 630 + -630 Combine like terms: 630 + -630 = 0 -630 + 12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-315 + 6x + x2) = 0 Factor a trinomial. 2((-21 + -1x)(15 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + -1x)' equal to zero and attempt to solve: Simplifying -21 + -1x = 0 Solving -21 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + -1x = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -1x = 0 + 21 -1x = 0 + 21 Combine like terms: 0 + 21 = 21 -1x = 21 Divide each side by '-1'. x = -21 Simplifying x = -21Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve: Simplifying 15 + -1x = 0 Solving 15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1x = 0 + -15 -1x = 0 + -15 Combine like terms: 0 + -15 = -15 -1x = -15 Divide each side by '-1'. x = 15 Simplifying x = 15Solution
x = {-21, 15}
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