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Simplifying (7x + -6)(x + 1) = (x + -2)(6x + 7) Reorder the terms: (-6 + 7x)(x + 1) = (x + -2)(6x + 7) Reorder the terms: (-6 + 7x)(1 + x) = (x + -2)(6x + 7) Multiply (-6 + 7x) * (1 + x) (-6(1 + x) + 7x * (1 + x)) = (x + -2)(6x + 7) ((1 * -6 + x * -6) + 7x * (1 + x)) = (x + -2)(6x + 7) ((-6 + -6x) + 7x * (1 + x)) = (x + -2)(6x + 7) (-6 + -6x + (1 * 7x + x * 7x)) = (x + -2)(6x + 7) (-6 + -6x + (7x + 7x2)) = (x + -2)(6x + 7) Combine like terms: -6x + 7x = 1x (-6 + 1x + 7x2) = (x + -2)(6x + 7) Reorder the terms: -6 + 1x + 7x2 = (-2 + x)(6x + 7) Reorder the terms: -6 + 1x + 7x2 = (-2 + x)(7 + 6x) Multiply (-2 + x) * (7 + 6x) -6 + 1x + 7x2 = (-2(7 + 6x) + x(7 + 6x)) -6 + 1x + 7x2 = ((7 * -2 + 6x * -2) + x(7 + 6x)) -6 + 1x + 7x2 = ((-14 + -12x) + x(7 + 6x)) -6 + 1x + 7x2 = (-14 + -12x + (7 * x + 6x * x)) -6 + 1x + 7x2 = (-14 + -12x + (7x + 6x2)) Combine like terms: -12x + 7x = -5x -6 + 1x + 7x2 = (-14 + -5x + 6x2) Solving -6 + 1x + 7x2 = -14 + -5x + 6x2 Solving for variable 'x'. Reorder the terms: -6 + 14 + 1x + 5x + 7x2 + -6x2 = -14 + -5x + 6x2 + 14 + 5x + -6x2 Combine like terms: -6 + 14 = 8 8 + 1x + 5x + 7x2 + -6x2 = -14 + -5x + 6x2 + 14 + 5x + -6x2 Combine like terms: 1x + 5x = 6x 8 + 6x + 7x2 + -6x2 = -14 + -5x + 6x2 + 14 + 5x + -6x2 Combine like terms: 7x2 + -6x2 = 1x2 8 + 6x + 1x2 = -14 + -5x + 6x2 + 14 + 5x + -6x2 Reorder the terms: 8 + 6x + 1x2 = -14 + 14 + -5x + 5x + 6x2 + -6x2 Combine like terms: -14 + 14 = 0 8 + 6x + 1x2 = 0 + -5x + 5x + 6x2 + -6x2 8 + 6x + 1x2 = -5x + 5x + 6x2 + -6x2 Combine like terms: -5x + 5x = 0 8 + 6x + 1x2 = 0 + 6x2 + -6x2 8 + 6x + 1x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 8 + 6x + 1x2 = 0 Factor a trinomial. (4 + x)(2 + x) = 0Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-4, -2}
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