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Simplifying (x + -7)(x + 5) = 2(x + 5) Reorder the terms: (-7 + x)(x + 5) = 2(x + 5) Reorder the terms: (-7 + x)(5 + x) = 2(x + 5) Multiply (-7 + x) * (5 + x) (-7(5 + x) + x(5 + x)) = 2(x + 5) ((5 * -7 + x * -7) + x(5 + x)) = 2(x + 5) ((-35 + -7x) + x(5 + x)) = 2(x + 5) (-35 + -7x + (5 * x + x * x)) = 2(x + 5) (-35 + -7x + (5x + x2)) = 2(x + 5) Combine like terms: -7x + 5x = -2x (-35 + -2x + x2) = 2(x + 5) Reorder the terms: -35 + -2x + x2 = 2(5 + x) -35 + -2x + x2 = (5 * 2 + x * 2) -35 + -2x + x2 = (10 + 2x) Solving -35 + -2x + x2 = 10 + 2x Solving for variable 'x'. Reorder the terms: -35 + -10 + -2x + -2x + x2 = 10 + 2x + -10 + -2x Combine like terms: -35 + -10 = -45 -45 + -2x + -2x + x2 = 10 + 2x + -10 + -2x Combine like terms: -2x + -2x = -4x -45 + -4x + x2 = 10 + 2x + -10 + -2x Reorder the terms: -45 + -4x + x2 = 10 + -10 + 2x + -2x Combine like terms: 10 + -10 = 0 -45 + -4x + x2 = 0 + 2x + -2x -45 + -4x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -45 + -4x + x2 = 0 Factor a trinomial. (-5 + -1x)(9 + -1x) = 0Subproblem 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 '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {-5, 9}
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