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Simplifying (2x + 2)(3x + 5) = 76x + -140 Reorder the terms: (2 + 2x)(3x + 5) = 76x + -140 Reorder the terms: (2 + 2x)(5 + 3x) = 76x + -140 Multiply (2 + 2x) * (5 + 3x) (2(5 + 3x) + 2x * (5 + 3x)) = 76x + -140 ((5 * 2 + 3x * 2) + 2x * (5 + 3x)) = 76x + -140 ((10 + 6x) + 2x * (5 + 3x)) = 76x + -140 (10 + 6x + (5 * 2x + 3x * 2x)) = 76x + -140 (10 + 6x + (10x + 6x2)) = 76x + -140 Combine like terms: 6x + 10x = 16x (10 + 16x + 6x2) = 76x + -140 Reorder the terms: 10 + 16x + 6x2 = -140 + 76x Solving 10 + 16x + 6x2 = -140 + 76x Solving for variable 'x'. Reorder the terms: 10 + 140 + 16x + -76x + 6x2 = -140 + 76x + 140 + -76x Combine like terms: 10 + 140 = 150 150 + 16x + -76x + 6x2 = -140 + 76x + 140 + -76x Combine like terms: 16x + -76x = -60x 150 + -60x + 6x2 = -140 + 76x + 140 + -76x Reorder the terms: 150 + -60x + 6x2 = -140 + 140 + 76x + -76x Combine like terms: -140 + 140 = 0 150 + -60x + 6x2 = 0 + 76x + -76x 150 + -60x + 6x2 = 76x + -76x Combine like terms: 76x + -76x = 0 150 + -60x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(25 + -10x + x2) = 0 Factor a trinomial. 6((5 + -1x)(5 + -1x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {5, 5}
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