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Simplifying (x + 7)(2x + -1) = (x + 7)(x + -2) Reorder the terms: (7 + x)(2x + -1) = (x + 7)(x + -2) Reorder the terms: (7 + x)(-1 + 2x) = (x + 7)(x + -2) Multiply (7 + x) * (-1 + 2x) (7(-1 + 2x) + x(-1 + 2x)) = (x + 7)(x + -2) ((-1 * 7 + 2x * 7) + x(-1 + 2x)) = (x + 7)(x + -2) ((-7 + 14x) + x(-1 + 2x)) = (x + 7)(x + -2) (-7 + 14x + (-1 * x + 2x * x)) = (x + 7)(x + -2) (-7 + 14x + (-1x + 2x2)) = (x + 7)(x + -2) Combine like terms: 14x + -1x = 13x (-7 + 13x + 2x2) = (x + 7)(x + -2) Reorder the terms: -7 + 13x + 2x2 = (7 + x)(x + -2) Reorder the terms: -7 + 13x + 2x2 = (7 + x)(-2 + x) Multiply (7 + x) * (-2 + x) -7 + 13x + 2x2 = (7(-2 + x) + x(-2 + x)) -7 + 13x + 2x2 = ((-2 * 7 + x * 7) + x(-2 + x)) -7 + 13x + 2x2 = ((-14 + 7x) + x(-2 + x)) -7 + 13x + 2x2 = (-14 + 7x + (-2 * x + x * x)) -7 + 13x + 2x2 = (-14 + 7x + (-2x + x2)) Combine like terms: 7x + -2x = 5x -7 + 13x + 2x2 = (-14 + 5x + x2) Solving -7 + 13x + 2x2 = -14 + 5x + x2 Solving for variable 'x'. Reorder the terms: -7 + 14 + 13x + -5x + 2x2 + -1x2 = -14 + 5x + x2 + 14 + -5x + -1x2 Combine like terms: -7 + 14 = 7 7 + 13x + -5x + 2x2 + -1x2 = -14 + 5x + x2 + 14 + -5x + -1x2 Combine like terms: 13x + -5x = 8x 7 + 8x + 2x2 + -1x2 = -14 + 5x + x2 + 14 + -5x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 7 + 8x + 1x2 = -14 + 5x + x2 + 14 + -5x + -1x2 Reorder the terms: 7 + 8x + 1x2 = -14 + 14 + 5x + -5x + x2 + -1x2 Combine like terms: -14 + 14 = 0 7 + 8x + 1x2 = 0 + 5x + -5x + x2 + -1x2 7 + 8x + 1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 7 + 8x + 1x2 = 0 + x2 + -1x2 7 + 8x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 7 + 8x + 1x2 = 0 Factor a trinomial. (7 + x)(1 + x) = 0Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {-7, -1}
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