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Simplifying (x + 4)(x + -4) = (2x + 5)(x + -4) Reorder the terms: (4 + x)(x + -4) = (2x + 5)(x + -4) Reorder the terms: (4 + x)(-4 + x) = (2x + 5)(x + -4) Multiply (4 + x) * (-4 + x) (4(-4 + x) + x(-4 + x)) = (2x + 5)(x + -4) ((-4 * 4 + x * 4) + x(-4 + x)) = (2x + 5)(x + -4) ((-16 + 4x) + x(-4 + x)) = (2x + 5)(x + -4) (-16 + 4x + (-4 * x + x * x)) = (2x + 5)(x + -4) (-16 + 4x + (-4x + x2)) = (2x + 5)(x + -4) Combine like terms: 4x + -4x = 0 (-16 + 0 + x2) = (2x + 5)(x + -4) (-16 + x2) = (2x + 5)(x + -4) Reorder the terms: -16 + x2 = (5 + 2x)(x + -4) Reorder the terms: -16 + x2 = (5 + 2x)(-4 + x) Multiply (5 + 2x) * (-4 + x) -16 + x2 = (5(-4 + x) + 2x * (-4 + x)) -16 + x2 = ((-4 * 5 + x * 5) + 2x * (-4 + x)) -16 + x2 = ((-20 + 5x) + 2x * (-4 + x)) -16 + x2 = (-20 + 5x + (-4 * 2x + x * 2x)) -16 + x2 = (-20 + 5x + (-8x + 2x2)) Combine like terms: 5x + -8x = -3x -16 + x2 = (-20 + -3x + 2x2) Solving -16 + x2 = -20 + -3x + 2x2 Solving for variable 'x'. Reorder the terms: -16 + 20 + 3x + x2 + -2x2 = -20 + -3x + 2x2 + 20 + 3x + -2x2 Combine like terms: -16 + 20 = 4 4 + 3x + x2 + -2x2 = -20 + -3x + 2x2 + 20 + 3x + -2x2 Combine like terms: x2 + -2x2 = -1x2 4 + 3x + -1x2 = -20 + -3x + 2x2 + 20 + 3x + -2x2 Reorder the terms: 4 + 3x + -1x2 = -20 + 20 + -3x + 3x + 2x2 + -2x2 Combine like terms: -20 + 20 = 0 4 + 3x + -1x2 = 0 + -3x + 3x + 2x2 + -2x2 4 + 3x + -1x2 = -3x + 3x + 2x2 + -2x2 Combine like terms: -3x + 3x = 0 4 + 3x + -1x2 = 0 + 2x2 + -2x2 4 + 3x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 4 + 3x + -1x2 = 0 Factor a trinomial. (4 + -1x)(1 + x) = 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {4, -1}
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