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Simplifying (2x + -1)(2x + 3) = 5 Reorder the terms: (-1 + 2x)(2x + 3) = 5 Reorder the terms: (-1 + 2x)(3 + 2x) = 5 Multiply (-1 + 2x) * (3 + 2x) (-1(3 + 2x) + 2x * (3 + 2x)) = 5 ((3 * -1 + 2x * -1) + 2x * (3 + 2x)) = 5 ((-3 + -2x) + 2x * (3 + 2x)) = 5 (-3 + -2x + (3 * 2x + 2x * 2x)) = 5 (-3 + -2x + (6x + 4x2)) = 5 Combine like terms: -2x + 6x = 4x (-3 + 4x + 4x2) = 5 Solving -3 + 4x + 4x2 = 5 Solving for variable 'x'. Reorder the terms: -3 + -5 + 4x + 4x2 = 5 + -5 Combine like terms: -3 + -5 = -8 -8 + 4x + 4x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -8 + 4x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-2 + x + x2) = 0 Factor a trinomial. 4((-2 + -1x)(1 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-2, 1}
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