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Simplifying (2x + 3)(2x + -3) + 5x = 2(x + 1) + -1 Reorder the terms: (3 + 2x)(2x + -3) + 5x = 2(x + 1) + -1 Reorder the terms: (3 + 2x)(-3 + 2x) + 5x = 2(x + 1) + -1 Multiply (3 + 2x) * (-3 + 2x) (3(-3 + 2x) + 2x * (-3 + 2x)) + 5x = 2(x + 1) + -1 ((-3 * 3 + 2x * 3) + 2x * (-3 + 2x)) + 5x = 2(x + 1) + -1 ((-9 + 6x) + 2x * (-3 + 2x)) + 5x = 2(x + 1) + -1 (-9 + 6x + (-3 * 2x + 2x * 2x)) + 5x = 2(x + 1) + -1 (-9 + 6x + (-6x + 4x2)) + 5x = 2(x + 1) + -1 Combine like terms: 6x + -6x = 0 (-9 + 0 + 4x2) + 5x = 2(x + 1) + -1 (-9 + 4x2) + 5x = 2(x + 1) + -1 Reorder the terms: -9 + 5x + 4x2 = 2(x + 1) + -1 Reorder the terms: -9 + 5x + 4x2 = 2(1 + x) + -1 -9 + 5x + 4x2 = (1 * 2 + x * 2) + -1 -9 + 5x + 4x2 = (2 + 2x) + -1 Reorder the terms: -9 + 5x + 4x2 = 2 + -1 + 2x Combine like terms: 2 + -1 = 1 -9 + 5x + 4x2 = 1 + 2x Solving -9 + 5x + 4x2 = 1 + 2x Solving for variable 'x'. Reorder the terms: -9 + -1 + 5x + -2x + 4x2 = 1 + 2x + -1 + -2x Combine like terms: -9 + -1 = -10 -10 + 5x + -2x + 4x2 = 1 + 2x + -1 + -2x Combine like terms: 5x + -2x = 3x -10 + 3x + 4x2 = 1 + 2x + -1 + -2x Reorder the terms: -10 + 3x + 4x2 = 1 + -1 + 2x + -2x Combine like terms: 1 + -1 = 0 -10 + 3x + 4x2 = 0 + 2x + -2x -10 + 3x + 4x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -10 + 3x + 4x2 = 0 Factor a trinomial. (-2 + -1x)(5 + -4x) = 0Subproblem 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 '(5 + -4x)' equal to zero and attempt to solve: Simplifying 5 + -4x = 0 Solving 5 + -4x = 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 + -4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x = 0 + -5 -4x = 0 + -5 Combine like terms: 0 + -5 = -5 -4x = -5 Divide each side by '-4'. x = 1.25 Simplifying x = 1.25Solution
x = {-2, 1.25}
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