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Simplifying (x + 9)(x + -4) = (2x + 1)(x + -4) Reorder the terms: (9 + x)(x + -4) = (2x + 1)(x + -4) Reorder the terms: (9 + x)(-4 + x) = (2x + 1)(x + -4) Multiply (9 + x) * (-4 + x) (9(-4 + x) + x(-4 + x)) = (2x + 1)(x + -4) ((-4 * 9 + x * 9) + x(-4 + x)) = (2x + 1)(x + -4) ((-36 + 9x) + x(-4 + x)) = (2x + 1)(x + -4) (-36 + 9x + (-4 * x + x * x)) = (2x + 1)(x + -4) (-36 + 9x + (-4x + x2)) = (2x + 1)(x + -4) Combine like terms: 9x + -4x = 5x (-36 + 5x + x2) = (2x + 1)(x + -4) Reorder the terms: -36 + 5x + x2 = (1 + 2x)(x + -4) Reorder the terms: -36 + 5x + x2 = (1 + 2x)(-4 + x) Multiply (1 + 2x) * (-4 + x) -36 + 5x + x2 = (1(-4 + x) + 2x * (-4 + x)) -36 + 5x + x2 = ((-4 * 1 + x * 1) + 2x * (-4 + x)) -36 + 5x + x2 = ((-4 + 1x) + 2x * (-4 + x)) -36 + 5x + x2 = (-4 + 1x + (-4 * 2x + x * 2x)) -36 + 5x + x2 = (-4 + 1x + (-8x + 2x2)) Combine like terms: 1x + -8x = -7x -36 + 5x + x2 = (-4 + -7x + 2x2) Solving -36 + 5x + x2 = -4 + -7x + 2x2 Solving for variable 'x'. Reorder the terms: -36 + 4 + 5x + 7x + x2 + -2x2 = -4 + -7x + 2x2 + 4 + 7x + -2x2 Combine like terms: -36 + 4 = -32 -32 + 5x + 7x + x2 + -2x2 = -4 + -7x + 2x2 + 4 + 7x + -2x2 Combine like terms: 5x + 7x = 12x -32 + 12x + x2 + -2x2 = -4 + -7x + 2x2 + 4 + 7x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -32 + 12x + -1x2 = -4 + -7x + 2x2 + 4 + 7x + -2x2 Reorder the terms: -32 + 12x + -1x2 = -4 + 4 + -7x + 7x + 2x2 + -2x2 Combine like terms: -4 + 4 = 0 -32 + 12x + -1x2 = 0 + -7x + 7x + 2x2 + -2x2 -32 + 12x + -1x2 = -7x + 7x + 2x2 + -2x2 Combine like terms: -7x + 7x = 0 -32 + 12x + -1x2 = 0 + 2x2 + -2x2 -32 + 12x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -32 + 12x + -1x2 = 0 Factor a trinomial. (-8 + x)(4 + -1x) = 0Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Simplifying x = 8Subproblem 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 = {8, 4}
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