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Simplifying (x + 6)(x + -4) = (2x + 7)(x + -4) Reorder the terms: (6 + x)(x + -4) = (2x + 7)(x + -4) Reorder the terms: (6 + x)(-4 + x) = (2x + 7)(x + -4) Multiply (6 + x) * (-4 + x) (6(-4 + x) + x(-4 + x)) = (2x + 7)(x + -4) ((-4 * 6 + x * 6) + x(-4 + x)) = (2x + 7)(x + -4) ((-24 + 6x) + x(-4 + x)) = (2x + 7)(x + -4) (-24 + 6x + (-4 * x + x * x)) = (2x + 7)(x + -4) (-24 + 6x + (-4x + x2)) = (2x + 7)(x + -4) Combine like terms: 6x + -4x = 2x (-24 + 2x + x2) = (2x + 7)(x + -4) Reorder the terms: -24 + 2x + x2 = (7 + 2x)(x + -4) Reorder the terms: -24 + 2x + x2 = (7 + 2x)(-4 + x) Multiply (7 + 2x) * (-4 + x) -24 + 2x + x2 = (7(-4 + x) + 2x * (-4 + x)) -24 + 2x + x2 = ((-4 * 7 + x * 7) + 2x * (-4 + x)) -24 + 2x + x2 = ((-28 + 7x) + 2x * (-4 + x)) -24 + 2x + x2 = (-28 + 7x + (-4 * 2x + x * 2x)) -24 + 2x + x2 = (-28 + 7x + (-8x + 2x2)) Combine like terms: 7x + -8x = -1x -24 + 2x + x2 = (-28 + -1x + 2x2) Solving -24 + 2x + x2 = -28 + -1x + 2x2 Solving for variable 'x'. Reorder the terms: -24 + 28 + 2x + x + x2 + -2x2 = -28 + -1x + 2x2 + 28 + x + -2x2 Combine like terms: -24 + 28 = 4 4 + 2x + x + x2 + -2x2 = -28 + -1x + 2x2 + 28 + x + -2x2 Combine like terms: 2x + x = 3x 4 + 3x + x2 + -2x2 = -28 + -1x + 2x2 + 28 + x + -2x2 Combine like terms: x2 + -2x2 = -1x2 4 + 3x + -1x2 = -28 + -1x + 2x2 + 28 + x + -2x2 Reorder the terms: 4 + 3x + -1x2 = -28 + 28 + -1x + x + 2x2 + -2x2 Combine like terms: -28 + 28 = 0 4 + 3x + -1x2 = 0 + -1x + x + 2x2 + -2x2 4 + 3x + -1x2 = -1x + x + 2x2 + -2x2 Combine like terms: -1x + x = 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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