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Simplifying x(x + 2) * 6 = 288 Reorder the terms: x(2 + x) * 6 = 288 Reorder the terms for easier multiplication: 6x(2 + x) = 288 (2 * 6x + x * 6x) = 288 (12x + 6x2) = 288 Solving 12x + 6x2 = 288 Solving for variable 'x'. Reorder the terms: -288 + 12x + 6x2 = 288 + -288 Combine like terms: 288 + -288 = 0 -288 + 12x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-48 + 2x + x2) = 0 Factor a trinomial. 6((-8 + -1x)(6 + -1x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve: Simplifying -8 + -1x = 0 Solving -8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1x = 0 + 8 -1x = 0 + 8 Combine like terms: 0 + 8 = 8 -1x = 8 Divide each side by '-1'. x = -8 Simplifying x = -8Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-8, 6}
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