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Simplifying (2x + 8)(5x + 7) = (8 + -3x)(2x + 8) Reorder the terms: (8 + 2x)(5x + 7) = (8 + -3x)(2x + 8) Reorder the terms: (8 + 2x)(7 + 5x) = (8 + -3x)(2x + 8) Multiply (8 + 2x) * (7 + 5x) (8(7 + 5x) + 2x * (7 + 5x)) = (8 + -3x)(2x + 8) ((7 * 8 + 5x * 8) + 2x * (7 + 5x)) = (8 + -3x)(2x + 8) ((56 + 40x) + 2x * (7 + 5x)) = (8 + -3x)(2x + 8) (56 + 40x + (7 * 2x + 5x * 2x)) = (8 + -3x)(2x + 8) (56 + 40x + (14x + 10x2)) = (8 + -3x)(2x + 8) Combine like terms: 40x + 14x = 54x (56 + 54x + 10x2) = (8 + -3x)(2x + 8) Reorder the terms: 56 + 54x + 10x2 = (8 + -3x)(8 + 2x) Multiply (8 + -3x) * (8 + 2x) 56 + 54x + 10x2 = (8(8 + 2x) + -3x * (8 + 2x)) 56 + 54x + 10x2 = ((8 * 8 + 2x * 8) + -3x * (8 + 2x)) 56 + 54x + 10x2 = ((64 + 16x) + -3x * (8 + 2x)) 56 + 54x + 10x2 = (64 + 16x + (8 * -3x + 2x * -3x)) 56 + 54x + 10x2 = (64 + 16x + (-24x + -6x2)) Combine like terms: 16x + -24x = -8x 56 + 54x + 10x2 = (64 + -8x + -6x2) Solving 56 + 54x + 10x2 = 64 + -8x + -6x2 Solving for variable 'x'. Reorder the terms: 56 + -64 + 54x + 8x + 10x2 + 6x2 = 64 + -8x + -6x2 + -64 + 8x + 6x2 Combine like terms: 56 + -64 = -8 -8 + 54x + 8x + 10x2 + 6x2 = 64 + -8x + -6x2 + -64 + 8x + 6x2 Combine like terms: 54x + 8x = 62x -8 + 62x + 10x2 + 6x2 = 64 + -8x + -6x2 + -64 + 8x + 6x2 Combine like terms: 10x2 + 6x2 = 16x2 -8 + 62x + 16x2 = 64 + -8x + -6x2 + -64 + 8x + 6x2 Reorder the terms: -8 + 62x + 16x2 = 64 + -64 + -8x + 8x + -6x2 + 6x2 Combine like terms: 64 + -64 = 0 -8 + 62x + 16x2 = 0 + -8x + 8x + -6x2 + 6x2 -8 + 62x + 16x2 = -8x + 8x + -6x2 + 6x2 Combine like terms: -8x + 8x = 0 -8 + 62x + 16x2 = 0 + -6x2 + 6x2 -8 + 62x + 16x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -8 + 62x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 31x + 8x2) = 0 Factor a trinomial. 2((-4 + -1x)(1 + -8x)) = 0 Ignore the factor 2.Subproblem 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 + -8x)' equal to zero and attempt to solve: Simplifying 1 + -8x = 0 Solving 1 + -8x = 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 + -8x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8x = 0 + -1 -8x = 0 + -1 Combine like terms: 0 + -1 = -1 -8x = -1 Divide each side by '-8'. x = 0.125 Simplifying x = 0.125Solution
x = {-4, 0.125}
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