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Simplifying (2x + -3)(5x + 2) + (3 + -1x)(2x + -3) = 0 Reorder the terms: (-3 + 2x)(5x + 2) + (3 + -1x)(2x + -3) = 0 Reorder the terms: (-3 + 2x)(2 + 5x) + (3 + -1x)(2x + -3) = 0 Multiply (-3 + 2x) * (2 + 5x) (-3(2 + 5x) + 2x * (2 + 5x)) + (3 + -1x)(2x + -3) = 0 ((2 * -3 + 5x * -3) + 2x * (2 + 5x)) + (3 + -1x)(2x + -3) = 0 ((-6 + -15x) + 2x * (2 + 5x)) + (3 + -1x)(2x + -3) = 0 (-6 + -15x + (2 * 2x + 5x * 2x)) + (3 + -1x)(2x + -3) = 0 (-6 + -15x + (4x + 10x2)) + (3 + -1x)(2x + -3) = 0 Combine like terms: -15x + 4x = -11x (-6 + -11x + 10x2) + (3 + -1x)(2x + -3) = 0 Reorder the terms: -6 + -11x + 10x2 + (3 + -1x)(-3 + 2x) = 0 Multiply (3 + -1x) * (-3 + 2x) -6 + -11x + 10x2 + (3(-3 + 2x) + -1x * (-3 + 2x)) = 0 -6 + -11x + 10x2 + ((-3 * 3 + 2x * 3) + -1x * (-3 + 2x)) = 0 -6 + -11x + 10x2 + ((-9 + 6x) + -1x * (-3 + 2x)) = 0 -6 + -11x + 10x2 + (-9 + 6x + (-3 * -1x + 2x * -1x)) = 0 -6 + -11x + 10x2 + (-9 + 6x + (3x + -2x2)) = 0 Combine like terms: 6x + 3x = 9x -6 + -11x + 10x2 + (-9 + 9x + -2x2) = 0 Reorder the terms: -6 + -9 + -11x + 9x + 10x2 + -2x2 = 0 Combine like terms: -6 + -9 = -15 -15 + -11x + 9x + 10x2 + -2x2 = 0 Combine like terms: -11x + 9x = -2x -15 + -2x + 10x2 + -2x2 = 0 Combine like terms: 10x2 + -2x2 = 8x2 -15 + -2x + 8x2 = 0 Solving -15 + -2x + 8x2 = 0 Solving for variable 'x'. Factor a trinomial. (-5 + -4x)(3 + -2x) = 0Subproblem 1
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 = -1.25Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {-1.25, 1.5}
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