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Simplifying (2x + 5)(x + -4) = (x + 7)(x + -4) Reorder the terms: (5 + 2x)(x + -4) = (x + 7)(x + -4) Reorder the terms: (5 + 2x)(-4 + x) = (x + 7)(x + -4) Multiply (5 + 2x) * (-4 + x) (5(-4 + x) + 2x * (-4 + x)) = (x + 7)(x + -4) ((-4 * 5 + x * 5) + 2x * (-4 + x)) = (x + 7)(x + -4) ((-20 + 5x) + 2x * (-4 + x)) = (x + 7)(x + -4) (-20 + 5x + (-4 * 2x + x * 2x)) = (x + 7)(x + -4) (-20 + 5x + (-8x + 2x2)) = (x + 7)(x + -4) Combine like terms: 5x + -8x = -3x (-20 + -3x + 2x2) = (x + 7)(x + -4) Reorder the terms: -20 + -3x + 2x2 = (7 + x)(x + -4) Reorder the terms: -20 + -3x + 2x2 = (7 + x)(-4 + x) Multiply (7 + x) * (-4 + x) -20 + -3x + 2x2 = (7(-4 + x) + x(-4 + x)) -20 + -3x + 2x2 = ((-4 * 7 + x * 7) + x(-4 + x)) -20 + -3x + 2x2 = ((-28 + 7x) + x(-4 + x)) -20 + -3x + 2x2 = (-28 + 7x + (-4 * x + x * x)) -20 + -3x + 2x2 = (-28 + 7x + (-4x + x2)) Combine like terms: 7x + -4x = 3x -20 + -3x + 2x2 = (-28 + 3x + x2) Solving -20 + -3x + 2x2 = -28 + 3x + x2 Solving for variable 'x'. Reorder the terms: -20 + 28 + -3x + -3x + 2x2 + -1x2 = -28 + 3x + x2 + 28 + -3x + -1x2 Combine like terms: -20 + 28 = 8 8 + -3x + -3x + 2x2 + -1x2 = -28 + 3x + x2 + 28 + -3x + -1x2 Combine like terms: -3x + -3x = -6x 8 + -6x + 2x2 + -1x2 = -28 + 3x + x2 + 28 + -3x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 8 + -6x + 1x2 = -28 + 3x + x2 + 28 + -3x + -1x2 Reorder the terms: 8 + -6x + 1x2 = -28 + 28 + 3x + -3x + x2 + -1x2 Combine like terms: -28 + 28 = 0 8 + -6x + 1x2 = 0 + 3x + -3x + x2 + -1x2 8 + -6x + 1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 8 + -6x + 1x2 = 0 + x2 + -1x2 8 + -6x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 8 + -6x + 1x2 = 0 Factor a trinomial. (2 + -1x)(4 + -1x) = 0Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 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 = {2, 4}
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