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Simplifying (x + -2)(2)((x + 10) + -2) = 832 Reorder the terms: (-2 + x)(2)((x + 10) + -2) = 832 Reorder the terms: (-2 + x) * 2((10 + x) + -2) = 832 Remove parenthesis around (10 + x) (-2 + x) * 2(10 + x + -2) = 832 Reorder the terms: (-2 + x) * 2(10 + -2 + x) = 832 Combine like terms: 10 + -2 = 8 (-2 + x) * 2(8 + x) = 832 Reorder the terms for easier multiplication: 2(-2 + x)(8 + x) = 832 Multiply (-2 + x) * (8 + x) 2(-2(8 + x) + x(8 + x)) = 832 2((8 * -2 + x * -2) + x(8 + x)) = 832 2((-16 + -2x) + x(8 + x)) = 832 2(-16 + -2x + (8 * x + x * x)) = 832 2(-16 + -2x + (8x + x2)) = 832 Combine like terms: -2x + 8x = 6x 2(-16 + 6x + x2) = 832 (-16 * 2 + 6x * 2 + x2 * 2) = 832 (-32 + 12x + 2x2) = 832 Solving -32 + 12x + 2x2 = 832 Solving for variable 'x'. Reorder the terms: -32 + -832 + 12x + 2x2 = 832 + -832 Combine like terms: -32 + -832 = -864 -864 + 12x + 2x2 = 832 + -832 Combine like terms: 832 + -832 = 0 -864 + 12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-432 + 6x + x2) = 0 Factor a trinomial. 2((-24 + -1x)(18 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-24 + -1x)' equal to zero and attempt to solve: Simplifying -24 + -1x = 0 Solving -24 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + -1x = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -1x = 0 + 24 -1x = 0 + 24 Combine like terms: 0 + 24 = 24 -1x = 24 Divide each side by '-1'. x = -24 Simplifying x = -24Subproblem 2
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 = 18Solution
x = {-24, 18}
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