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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 = -15x -24 + 2x + x2 = (28 + -15x + 2x2) Solving -24 + 2x + x2 = 28 + -15x + 2x2 Solving for variable 'x'. Reorder the terms: -24 + -28 + 2x + 15x + x2 + -2x2 = 28 + -15x + 2x2 + -28 + 15x + -2x2 Combine like terms: -24 + -28 = -52 -52 + 2x + 15x + x2 + -2x2 = 28 + -15x + 2x2 + -28 + 15x + -2x2 Combine like terms: 2x + 15x = 17x -52 + 17x + x2 + -2x2 = 28 + -15x + 2x2 + -28 + 15x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -52 + 17x + -1x2 = 28 + -15x + 2x2 + -28 + 15x + -2x2 Reorder the terms: -52 + 17x + -1x2 = 28 + -28 + -15x + 15x + 2x2 + -2x2 Combine like terms: 28 + -28 = 0 -52 + 17x + -1x2 = 0 + -15x + 15x + 2x2 + -2x2 -52 + 17x + -1x2 = -15x + 15x + 2x2 + -2x2 Combine like terms: -15x + 15x = 0 -52 + 17x + -1x2 = 0 + 2x2 + -2x2 -52 + 17x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -52 + 17x + -1x2 = 0 Factor a trinomial. (-13 + x)(4 + -1x) = 0Subproblem 1
Set the factor '(-13 + x)' equal to zero and attempt to solve: Simplifying -13 + x = 0 Solving -13 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + x = 0 + 13 x = 0 + 13 Combine like terms: 0 + 13 = 13 x = 13 Simplifying x = 13Subproblem 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 = {13, 4}
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