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Simplifying (2x + 4)(x + 6) = 384 Reorder the terms: (4 + 2x)(x + 6) = 384 Reorder the terms: (4 + 2x)(6 + x) = 384 Multiply (4 + 2x) * (6 + x) (4(6 + x) + 2x * (6 + x)) = 384 ((6 * 4 + x * 4) + 2x * (6 + x)) = 384 ((24 + 4x) + 2x * (6 + x)) = 384 (24 + 4x + (6 * 2x + x * 2x)) = 384 (24 + 4x + (12x + 2x2)) = 384 Combine like terms: 4x + 12x = 16x (24 + 16x + 2x2) = 384 Solving 24 + 16x + 2x2 = 384 Solving for variable 'x'. Reorder the terms: 24 + -384 + 16x + 2x2 = 384 + -384 Combine like terms: 24 + -384 = -360 -360 + 16x + 2x2 = 384 + -384 Combine like terms: 384 + -384 = 0 -360 + 16x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-180 + 8x + x2) = 0 Factor a trinomial. 2((-18 + -1x)(10 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-18 + -1x)' equal to zero and attempt to solve: Simplifying -18 + -1x = 0 Solving -18 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + -1x = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -1x = 0 + 18 -1x = 0 + 18 Combine like terms: 0 + 18 = 18 -1x = 18 Divide each side by '-1'. x = -18 Simplifying x = -18Subproblem 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 = {-18, 10}
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