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Simplifying (2x + -6)(x + 8) = (20)(39) Reorder the terms: (-6 + 2x)(x + 8) = (20)(39) Reorder the terms: (-6 + 2x)(8 + x) = (20)(39) Multiply (-6 + 2x) * (8 + x) (-6(8 + x) + 2x * (8 + x)) = (20)(39) ((8 * -6 + x * -6) + 2x * (8 + x)) = (20)(39) ((-48 + -6x) + 2x * (8 + x)) = (20)(39) (-48 + -6x + (8 * 2x + x * 2x)) = (20)(39) (-48 + -6x + (16x + 2x2)) = (20)(39) Combine like terms: -6x + 16x = 10x (-48 + 10x + 2x2) = (20)(39) Multiply 20 * 39 -48 + 10x + 2x2 = 780 Solving -48 + 10x + 2x2 = 780 Solving for variable 'x'. Reorder the terms: -48 + -780 + 10x + 2x2 = 780 + -780 Combine like terms: -48 + -780 = -828 -828 + 10x + 2x2 = 780 + -780 Combine like terms: 780 + -780 = 0 -828 + 10x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-414 + 5x + x2) = 0 Factor a trinomial. 2((-23 + -1x)(18 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-23 + -1x)' equal to zero and attempt to solve: Simplifying -23 + -1x = 0 Solving -23 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + -1x = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -1x = 0 + 23 -1x = 0 + 23 Combine like terms: 0 + 23 = 23 -1x = 23 Divide each side by '-1'. x = -23 Simplifying x = -23Subproblem 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 = {-23, 18}
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