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Simplifying (x + 3)(x + -4) + -1(x + 2)(4 + -1x) = 0 Reorder the terms: (3 + x)(x + -4) + -1(x + 2)(4 + -1x) = 0 Reorder the terms: (3 + x)(-4 + x) + -1(x + 2)(4 + -1x) = 0 Multiply (3 + x) * (-4 + x) (3(-4 + x) + x(-4 + x)) + -1(x + 2)(4 + -1x) = 0 ((-4 * 3 + x * 3) + x(-4 + x)) + -1(x + 2)(4 + -1x) = 0 ((-12 + 3x) + x(-4 + x)) + -1(x + 2)(4 + -1x) = 0 (-12 + 3x + (-4 * x + x * x)) + -1(x + 2)(4 + -1x) = 0 (-12 + 3x + (-4x + x2)) + -1(x + 2)(4 + -1x) = 0 Combine like terms: 3x + -4x = -1x (-12 + -1x + x2) + -1(x + 2)(4 + -1x) = 0 Reorder the terms: -12 + -1x + x2 + -1(2 + x)(4 + -1x) = 0 Multiply (2 + x) * (4 + -1x) -12 + -1x + x2 + -1(2(4 + -1x) + x(4 + -1x)) = 0 -12 + -1x + x2 + -1((4 * 2 + -1x * 2) + x(4 + -1x)) = 0 -12 + -1x + x2 + -1((8 + -2x) + x(4 + -1x)) = 0 -12 + -1x + x2 + -1(8 + -2x + (4 * x + -1x * x)) = 0 -12 + -1x + x2 + -1(8 + -2x + (4x + -1x2)) = 0 Combine like terms: -2x + 4x = 2x -12 + -1x + x2 + -1(8 + 2x + -1x2) = 0 -12 + -1x + x2 + (8 * -1 + 2x * -1 + -1x2 * -1) = 0 -12 + -1x + x2 + (-8 + -2x + 1x2) = 0 Reorder the terms: -12 + -8 + -1x + -2x + x2 + 1x2 = 0 Combine like terms: -12 + -8 = -20 -20 + -1x + -2x + x2 + 1x2 = 0 Combine like terms: -1x + -2x = -3x -20 + -3x + x2 + 1x2 = 0 Combine like terms: x2 + 1x2 = 2x2 -20 + -3x + 2x2 = 0 Solving -20 + -3x + 2x2 = 0 Solving for variable 'x'. Factor a trinomial. (-5 + -2x)(4 + -1x) = 0Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve: Simplifying -5 + -2x = 0 Solving -5 + -2x = 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 + -2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x = 0 + 5 -2x = 0 + 5 Combine like terms: 0 + 5 = 5 -2x = 5 Divide each side by '-2'. x = -2.5 Simplifying x = -2.5Subproblem 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 = {-2.5, 4}
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