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Simplifying (x + -4)(x + 2) + -1(x + -4)(2x + -3) = 0 Reorder the terms: (-4 + x)(x + 2) + -1(x + -4)(2x + -3) = 0 Reorder the terms: (-4 + x)(2 + x) + -1(x + -4)(2x + -3) = 0 Multiply (-4 + x) * (2 + x) (-4(2 + x) + x(2 + x)) + -1(x + -4)(2x + -3) = 0 ((2 * -4 + x * -4) + x(2 + x)) + -1(x + -4)(2x + -3) = 0 ((-8 + -4x) + x(2 + x)) + -1(x + -4)(2x + -3) = 0 (-8 + -4x + (2 * x + x * x)) + -1(x + -4)(2x + -3) = 0 (-8 + -4x + (2x + x2)) + -1(x + -4)(2x + -3) = 0 Combine like terms: -4x + 2x = -2x (-8 + -2x + x2) + -1(x + -4)(2x + -3) = 0 Reorder the terms: -8 + -2x + x2 + -1(-4 + x)(2x + -3) = 0 Reorder the terms: -8 + -2x + x2 + -1(-4 + x)(-3 + 2x) = 0 Multiply (-4 + x) * (-3 + 2x) -8 + -2x + x2 + -1(-4(-3 + 2x) + x(-3 + 2x)) = 0 -8 + -2x + x2 + -1((-3 * -4 + 2x * -4) + x(-3 + 2x)) = 0 -8 + -2x + x2 + -1((12 + -8x) + x(-3 + 2x)) = 0 -8 + -2x + x2 + -1(12 + -8x + (-3 * x + 2x * x)) = 0 -8 + -2x + x2 + -1(12 + -8x + (-3x + 2x2)) = 0 Combine like terms: -8x + -3x = -11x -8 + -2x + x2 + -1(12 + -11x + 2x2) = 0 -8 + -2x + x2 + (12 * -1 + -11x * -1 + 2x2 * -1) = 0 -8 + -2x + x2 + (-12 + 11x + -2x2) = 0 Reorder the terms: -8 + -12 + -2x + 11x + x2 + -2x2 = 0 Combine like terms: -8 + -12 = -20 -20 + -2x + 11x + x2 + -2x2 = 0 Combine like terms: -2x + 11x = 9x -20 + 9x + x2 + -2x2 = 0 Combine like terms: x2 + -2x2 = -1x2 -20 + 9x + -1x2 = 0 Solving -20 + 9x + -1x2 = 0 Solving for variable 'x'. Factor a trinomial. (-5 + x)(4 + -1x) = 0Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 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 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {5, 4}
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