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Simplifying (x + 6)(x + 2) = 140 Reorder the terms: (6 + x)(x + 2) = 140 Reorder the terms: (6 + x)(2 + x) = 140 Multiply (6 + x) * (2 + x) (6(2 + x) + x(2 + x)) = 140 ((2 * 6 + x * 6) + x(2 + x)) = 140 ((12 + 6x) + x(2 + x)) = 140 (12 + 6x + (2 * x + x * x)) = 140 (12 + 6x + (2x + x2)) = 140 Combine like terms: 6x + 2x = 8x (12 + 8x + x2) = 140 Solving 12 + 8x + x2 = 140 Solving for variable 'x'. Reorder the terms: 12 + -140 + 8x + x2 = 140 + -140 Combine like terms: 12 + -140 = -128 -128 + 8x + x2 = 140 + -140 Combine like terms: 140 + -140 = 0 -128 + 8x + x2 = 0 Factor a trinomial. (-16 + -1x)(8 + -1x) = 0Subproblem 1
Set the factor '(-16 + -1x)' equal to zero and attempt to solve: Simplifying -16 + -1x = 0 Solving -16 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + -1x = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -1x = 0 + 16 -1x = 0 + 16 Combine like terms: 0 + 16 = 16 -1x = 16 Divide each side by '-1'. x = -16 Simplifying x = -16Subproblem 2
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 = 8Solution
x = {-16, 8}
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