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Simplifying (3x + 2)(x + 6) = (2x + 3)(x + 8) Reorder the terms: (2 + 3x)(x + 6) = (2x + 3)(x + 8) Reorder the terms: (2 + 3x)(6 + x) = (2x + 3)(x + 8) Multiply (2 + 3x) * (6 + x) (2(6 + x) + 3x * (6 + x)) = (2x + 3)(x + 8) ((6 * 2 + x * 2) + 3x * (6 + x)) = (2x + 3)(x + 8) ((12 + 2x) + 3x * (6 + x)) = (2x + 3)(x + 8) (12 + 2x + (6 * 3x + x * 3x)) = (2x + 3)(x + 8) (12 + 2x + (18x + 3x2)) = (2x + 3)(x + 8) Combine like terms: 2x + 18x = 20x (12 + 20x + 3x2) = (2x + 3)(x + 8) Reorder the terms: 12 + 20x + 3x2 = (3 + 2x)(x + 8) Reorder the terms: 12 + 20x + 3x2 = (3 + 2x)(8 + x) Multiply (3 + 2x) * (8 + x) 12 + 20x + 3x2 = (3(8 + x) + 2x * (8 + x)) 12 + 20x + 3x2 = ((8 * 3 + x * 3) + 2x * (8 + x)) 12 + 20x + 3x2 = ((24 + 3x) + 2x * (8 + x)) 12 + 20x + 3x2 = (24 + 3x + (8 * 2x + x * 2x)) 12 + 20x + 3x2 = (24 + 3x + (16x + 2x2)) Combine like terms: 3x + 16x = 19x 12 + 20x + 3x2 = (24 + 19x + 2x2) Solving 12 + 20x + 3x2 = 24 + 19x + 2x2 Solving for variable 'x'. Reorder the terms: 12 + -24 + 20x + -19x + 3x2 + -2x2 = 24 + 19x + 2x2 + -24 + -19x + -2x2 Combine like terms: 12 + -24 = -12 -12 + 20x + -19x + 3x2 + -2x2 = 24 + 19x + 2x2 + -24 + -19x + -2x2 Combine like terms: 20x + -19x = 1x -12 + 1x + 3x2 + -2x2 = 24 + 19x + 2x2 + -24 + -19x + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 -12 + 1x + 1x2 = 24 + 19x + 2x2 + -24 + -19x + -2x2 Reorder the terms: -12 + 1x + 1x2 = 24 + -24 + 19x + -19x + 2x2 + -2x2 Combine like terms: 24 + -24 = 0 -12 + 1x + 1x2 = 0 + 19x + -19x + 2x2 + -2x2 -12 + 1x + 1x2 = 19x + -19x + 2x2 + -2x2 Combine like terms: 19x + -19x = 0 -12 + 1x + 1x2 = 0 + 2x2 + -2x2 -12 + 1x + 1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -12 + 1x + 1x2 = 0 Factor a trinomial. (-4 + -1x)(3 + -1x) = 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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-4, 3}
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