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Simplifying 5x + 7 = (3x + 2)(x + -1) Reorder the terms: 7 + 5x = (3x + 2)(x + -1) Reorder the terms: 7 + 5x = (2 + 3x)(x + -1) Reorder the terms: 7 + 5x = (2 + 3x)(-1 + x) Multiply (2 + 3x) * (-1 + x) 7 + 5x = (2(-1 + x) + 3x * (-1 + x)) 7 + 5x = ((-1 * 2 + x * 2) + 3x * (-1 + x)) 7 + 5x = ((-2 + 2x) + 3x * (-1 + x)) 7 + 5x = (-2 + 2x + (-1 * 3x + x * 3x)) 7 + 5x = (-2 + 2x + (-3x + 3x2)) Combine like terms: 2x + -3x = -1x 7 + 5x = (-2 + -1x + 3x2) Solving 7 + 5x = -2 + -1x + 3x2 Solving for variable 'x'. Reorder the terms: 7 + 2 + 5x + x + -3x2 = -2 + -1x + 3x2 + 2 + x + -3x2 Combine like terms: 7 + 2 = 9 9 + 5x + x + -3x2 = -2 + -1x + 3x2 + 2 + x + -3x2 Combine like terms: 5x + x = 6x 9 + 6x + -3x2 = -2 + -1x + 3x2 + 2 + x + -3x2 Reorder the terms: 9 + 6x + -3x2 = -2 + 2 + -1x + x + 3x2 + -3x2 Combine like terms: -2 + 2 = 0 9 + 6x + -3x2 = 0 + -1x + x + 3x2 + -3x2 9 + 6x + -3x2 = -1x + x + 3x2 + -3x2 Combine like terms: -1x + x = 0 9 + 6x + -3x2 = 0 + 3x2 + -3x2 9 + 6x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 9 + 6x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3 + 2x + -1x2) = 0 Factor a trinomial. 3((3 + -1x)(1 + x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {3, -1}
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