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Simplifying (x + -2)(2x + -3) + -1(x + 5)(x + -2) = 0 Reorder the terms: (-2 + x)(2x + -3) + -1(x + 5)(x + -2) = 0 Reorder the terms: (-2 + x)(-3 + 2x) + -1(x + 5)(x + -2) = 0 Multiply (-2 + x) * (-3 + 2x) (-2(-3 + 2x) + x(-3 + 2x)) + -1(x + 5)(x + -2) = 0 ((-3 * -2 + 2x * -2) + x(-3 + 2x)) + -1(x + 5)(x + -2) = 0 ((6 + -4x) + x(-3 + 2x)) + -1(x + 5)(x + -2) = 0 (6 + -4x + (-3 * x + 2x * x)) + -1(x + 5)(x + -2) = 0 (6 + -4x + (-3x + 2x2)) + -1(x + 5)(x + -2) = 0 Combine like terms: -4x + -3x = -7x (6 + -7x + 2x2) + -1(x + 5)(x + -2) = 0 Reorder the terms: 6 + -7x + 2x2 + -1(5 + x)(x + -2) = 0 Reorder the terms: 6 + -7x + 2x2 + -1(5 + x)(-2 + x) = 0 Multiply (5 + x) * (-2 + x) 6 + -7x + 2x2 + -1(5(-2 + x) + x(-2 + x)) = 0 6 + -7x + 2x2 + -1((-2 * 5 + x * 5) + x(-2 + x)) = 0 6 + -7x + 2x2 + -1((-10 + 5x) + x(-2 + x)) = 0 6 + -7x + 2x2 + -1(-10 + 5x + (-2 * x + x * x)) = 0 6 + -7x + 2x2 + -1(-10 + 5x + (-2x + x2)) = 0 Combine like terms: 5x + -2x = 3x 6 + -7x + 2x2 + -1(-10 + 3x + x2) = 0 6 + -7x + 2x2 + (-10 * -1 + 3x * -1 + x2 * -1) = 0 6 + -7x + 2x2 + (10 + -3x + -1x2) = 0 Reorder the terms: 6 + 10 + -7x + -3x + 2x2 + -1x2 = 0 Combine like terms: 6 + 10 = 16 16 + -7x + -3x + 2x2 + -1x2 = 0 Combine like terms: -7x + -3x = -10x 16 + -10x + 2x2 + -1x2 = 0 Combine like terms: 2x2 + -1x2 = 1x2 16 + -10x + 1x2 = 0 Solving 16 + -10x + 1x2 = 0 Solving for variable 'x'. Factor a trinomial. (2 + -1x)(8 + -1x) = 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 '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {2, 8}
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