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Simplifying (x + 1)(x + 2) = 6(x + x + 1) + -12 Reorder the terms: (1 + x)(x + 2) = 6(x + x + 1) + -12 Reorder the terms: (1 + x)(2 + x) = 6(x + x + 1) + -12 Multiply (1 + x) * (2 + x) (1(2 + x) + x(2 + x)) = 6(x + x + 1) + -12 ((2 * 1 + x * 1) + x(2 + x)) = 6(x + x + 1) + -12 ((2 + 1x) + x(2 + x)) = 6(x + x + 1) + -12 (2 + 1x + (2 * x + x * x)) = 6(x + x + 1) + -12 (2 + 1x + (2x + x2)) = 6(x + x + 1) + -12 Combine like terms: 1x + 2x = 3x (2 + 3x + x2) = 6(x + x + 1) + -12 Reorder the terms: 2 + 3x + x2 = 6(1 + x + x) + -12 Combine like terms: x + x = 2x 2 + 3x + x2 = 6(1 + 2x) + -12 2 + 3x + x2 = (1 * 6 + 2x * 6) + -12 2 + 3x + x2 = (6 + 12x) + -12 Reorder the terms: 2 + 3x + x2 = 6 + -12 + 12x Combine like terms: 6 + -12 = -6 2 + 3x + x2 = -6 + 12x Solving 2 + 3x + x2 = -6 + 12x Solving for variable 'x'. Reorder the terms: 2 + 6 + 3x + -12x + x2 = -6 + 12x + 6 + -12x Combine like terms: 2 + 6 = 8 8 + 3x + -12x + x2 = -6 + 12x + 6 + -12x Combine like terms: 3x + -12x = -9x 8 + -9x + x2 = -6 + 12x + 6 + -12x Reorder the terms: 8 + -9x + x2 = -6 + 6 + 12x + -12x Combine like terms: -6 + 6 = 0 8 + -9x + x2 = 0 + 12x + -12x 8 + -9x + x2 = 12x + -12x Combine like terms: 12x + -12x = 0 8 + -9x + x2 = 0 Factor a trinomial. (1 + -1x)(8 + -1x) = 0Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {1, 8}
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