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Simplifying (x + -2)(3x + 5) + (x + -2)(5x + -4) = 0 Reorder the terms: (-2 + x)(3x + 5) + (x + -2)(5x + -4) = 0 Reorder the terms: (-2 + x)(5 + 3x) + (x + -2)(5x + -4) = 0 Multiply (-2 + x) * (5 + 3x) (-2(5 + 3x) + x(5 + 3x)) + (x + -2)(5x + -4) = 0 ((5 * -2 + 3x * -2) + x(5 + 3x)) + (x + -2)(5x + -4) = 0 ((-10 + -6x) + x(5 + 3x)) + (x + -2)(5x + -4) = 0 (-10 + -6x + (5 * x + 3x * x)) + (x + -2)(5x + -4) = 0 (-10 + -6x + (5x + 3x2)) + (x + -2)(5x + -4) = 0 Combine like terms: -6x + 5x = -1x (-10 + -1x + 3x2) + (x + -2)(5x + -4) = 0 Reorder the terms: -10 + -1x + 3x2 + (-2 + x)(5x + -4) = 0 Reorder the terms: -10 + -1x + 3x2 + (-2 + x)(-4 + 5x) = 0 Multiply (-2 + x) * (-4 + 5x) -10 + -1x + 3x2 + (-2(-4 + 5x) + x(-4 + 5x)) = 0 -10 + -1x + 3x2 + ((-4 * -2 + 5x * -2) + x(-4 + 5x)) = 0 -10 + -1x + 3x2 + ((8 + -10x) + x(-4 + 5x)) = 0 -10 + -1x + 3x2 + (8 + -10x + (-4 * x + 5x * x)) = 0 -10 + -1x + 3x2 + (8 + -10x + (-4x + 5x2)) = 0 Combine like terms: -10x + -4x = -14x -10 + -1x + 3x2 + (8 + -14x + 5x2) = 0 Reorder the terms: -10 + 8 + -1x + -14x + 3x2 + 5x2 = 0 Combine like terms: -10 + 8 = -2 -2 + -1x + -14x + 3x2 + 5x2 = 0 Combine like terms: -1x + -14x = -15x -2 + -15x + 3x2 + 5x2 = 0 Combine like terms: 3x2 + 5x2 = 8x2 -2 + -15x + 8x2 = 0 Solving -2 + -15x + 8x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -8x)(2 + -1x) = 0Subproblem 1
Set the factor '(-1 + -8x)' equal to zero and attempt to solve: Simplifying -1 + -8x = 0 Solving -1 + -8x = 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 + -8x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -8x = 0 + 1 -8x = 0 + 1 Combine like terms: 0 + 1 = 1 -8x = 1 Divide each side by '-8'. x = -0.125 Simplifying x = -0.125Subproblem 2
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 = 2Solution
x = {-0.125, 2}
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