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Simplifying (x + -4)(x + -4) = (x + -4)(2x + -1) Reorder the terms: (-4 + x)(x + -4) = (x + -4)(2x + -1) Reorder the terms: (-4 + x)(-4 + x) = (x + -4)(2x + -1) Multiply (-4 + x) * (-4 + x) (-4(-4 + x) + x(-4 + x)) = (x + -4)(2x + -1) ((-4 * -4 + x * -4) + x(-4 + x)) = (x + -4)(2x + -1) ((16 + -4x) + x(-4 + x)) = (x + -4)(2x + -1) (16 + -4x + (-4 * x + x * x)) = (x + -4)(2x + -1) (16 + -4x + (-4x + x2)) = (x + -4)(2x + -1) Combine like terms: -4x + -4x = -8x (16 + -8x + x2) = (x + -4)(2x + -1) Reorder the terms: 16 + -8x + x2 = (-4 + x)(2x + -1) Reorder the terms: 16 + -8x + x2 = (-4 + x)(-1 + 2x) Multiply (-4 + x) * (-1 + 2x) 16 + -8x + x2 = (-4(-1 + 2x) + x(-1 + 2x)) 16 + -8x + x2 = ((-1 * -4 + 2x * -4) + x(-1 + 2x)) 16 + -8x + x2 = ((4 + -8x) + x(-1 + 2x)) 16 + -8x + x2 = (4 + -8x + (-1 * x + 2x * x)) 16 + -8x + x2 = (4 + -8x + (-1x + 2x2)) Combine like terms: -8x + -1x = -9x 16 + -8x + x2 = (4 + -9x + 2x2) Solving 16 + -8x + x2 = 4 + -9x + 2x2 Solving for variable 'x'. Reorder the terms: 16 + -4 + -8x + 9x + x2 + -2x2 = 4 + -9x + 2x2 + -4 + 9x + -2x2 Combine like terms: 16 + -4 = 12 12 + -8x + 9x + x2 + -2x2 = 4 + -9x + 2x2 + -4 + 9x + -2x2 Combine like terms: -8x + 9x = 1x 12 + 1x + x2 + -2x2 = 4 + -9x + 2x2 + -4 + 9x + -2x2 Combine like terms: x2 + -2x2 = -1x2 12 + 1x + -1x2 = 4 + -9x + 2x2 + -4 + 9x + -2x2 Reorder the terms: 12 + 1x + -1x2 = 4 + -4 + -9x + 9x + 2x2 + -2x2 Combine like terms: 4 + -4 = 0 12 + 1x + -1x2 = 0 + -9x + 9x + 2x2 + -2x2 12 + 1x + -1x2 = -9x + 9x + 2x2 + -2x2 Combine like terms: -9x + 9x = 0 12 + 1x + -1x2 = 0 + 2x2 + -2x2 12 + 1x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 12 + 1x + -1x2 = 0 Factor a trinomial. (4 + -1x)(3 + 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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {4, -3}
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