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Simplifying x(x + 2)(6) = 378 Reorder the terms: x(2 + x)(6) = 378 Reorder the terms for easier multiplication: 6x(2 + x) = 378 (2 * 6x + x * 6x) = 378 (12x + 6x2) = 378 Solving 12x + 6x2 = 378 Solving for variable 'x'. Reorder the terms: -378 + 12x + 6x2 = 378 + -378 Combine like terms: 378 + -378 = 0 -378 + 12x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-63 + 2x + x2) = 0 Factor a trinomial. 6((-9 + -1x)(7 + -1x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {-9, 7}
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