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Simplifying (2x + 4)(x + 4) = 160 Reorder the terms: (4 + 2x)(x + 4) = 160 Reorder the terms: (4 + 2x)(4 + x) = 160 Multiply (4 + 2x) * (4 + x) (4(4 + x) + 2x * (4 + x)) = 160 ((4 * 4 + x * 4) + 2x * (4 + x)) = 160 ((16 + 4x) + 2x * (4 + x)) = 160 (16 + 4x + (4 * 2x + x * 2x)) = 160 (16 + 4x + (8x + 2x2)) = 160 Combine like terms: 4x + 8x = 12x (16 + 12x + 2x2) = 160 Solving 16 + 12x + 2x2 = 160 Solving for variable 'x'. Reorder the terms: 16 + -160 + 12x + 2x2 = 160 + -160 Combine like terms: 16 + -160 = -144 -144 + 12x + 2x2 = 160 + -160 Combine like terms: 160 + -160 = 0 -144 + 12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-72 + 6x + x2) = 0 Factor a trinomial. 2((-12 + -1x)(6 + -1x)) = 0 Ignore the factor 2.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 '(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 = {-12, 6}
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