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Simplifying (x + 4)(2x + -5) + -1(x + 4)(x + 1) = 0 Reorder the terms: (4 + x)(2x + -5) + -1(x + 4)(x + 1) = 0 Reorder the terms: (4 + x)(-5 + 2x) + -1(x + 4)(x + 1) = 0 Multiply (4 + x) * (-5 + 2x) (4(-5 + 2x) + x(-5 + 2x)) + -1(x + 4)(x + 1) = 0 ((-5 * 4 + 2x * 4) + x(-5 + 2x)) + -1(x + 4)(x + 1) = 0 ((-20 + 8x) + x(-5 + 2x)) + -1(x + 4)(x + 1) = 0 (-20 + 8x + (-5 * x + 2x * x)) + -1(x + 4)(x + 1) = 0 (-20 + 8x + (-5x + 2x2)) + -1(x + 4)(x + 1) = 0 Combine like terms: 8x + -5x = 3x (-20 + 3x + 2x2) + -1(x + 4)(x + 1) = 0 Reorder the terms: -20 + 3x + 2x2 + -1(4 + x)(x + 1) = 0 Reorder the terms: -20 + 3x + 2x2 + -1(4 + x)(1 + x) = 0 Multiply (4 + x) * (1 + x) -20 + 3x + 2x2 + -1(4(1 + x) + x(1 + x)) = 0 -20 + 3x + 2x2 + -1((1 * 4 + x * 4) + x(1 + x)) = 0 -20 + 3x + 2x2 + -1((4 + 4x) + x(1 + x)) = 0 -20 + 3x + 2x2 + -1(4 + 4x + (1 * x + x * x)) = 0 -20 + 3x + 2x2 + -1(4 + 4x + (1x + x2)) = 0 Combine like terms: 4x + 1x = 5x -20 + 3x + 2x2 + -1(4 + 5x + x2) = 0 -20 + 3x + 2x2 + (4 * -1 + 5x * -1 + x2 * -1) = 0 -20 + 3x + 2x2 + (-4 + -5x + -1x2) = 0 Reorder the terms: -20 + -4 + 3x + -5x + 2x2 + -1x2 = 0 Combine like terms: -20 + -4 = -24 -24 + 3x + -5x + 2x2 + -1x2 = 0 Combine like terms: 3x + -5x = -2x -24 + -2x + 2x2 + -1x2 = 0 Combine like terms: 2x2 + -1x2 = 1x2 -24 + -2x + 1x2 = 0 Solving -24 + -2x + 1x2 = 0 Solving for variable 'x'. Factor a trinomial. (-4 + -1x)(6 + -1x) = 0Subproblem 1
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 = -4Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-4, 6}
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