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Simplifying (x + -6)(x + -1) = (2x + 1)(x + -1) Reorder the terms: (-6 + x)(x + -1) = (2x + 1)(x + -1) Reorder the terms: (-6 + x)(-1 + x) = (2x + 1)(x + -1) Multiply (-6 + x) * (-1 + x) (-6(-1 + x) + x(-1 + x)) = (2x + 1)(x + -1) ((-1 * -6 + x * -6) + x(-1 + x)) = (2x + 1)(x + -1) ((6 + -6x) + x(-1 + x)) = (2x + 1)(x + -1) (6 + -6x + (-1 * x + x * x)) = (2x + 1)(x + -1) (6 + -6x + (-1x + x2)) = (2x + 1)(x + -1) Combine like terms: -6x + -1x = -7x (6 + -7x + x2) = (2x + 1)(x + -1) Reorder the terms: 6 + -7x + x2 = (1 + 2x)(x + -1) Reorder the terms: 6 + -7x + x2 = (1 + 2x)(-1 + x) Multiply (1 + 2x) * (-1 + x) 6 + -7x + x2 = (1(-1 + x) + 2x * (-1 + x)) 6 + -7x + x2 = ((-1 * 1 + x * 1) + 2x * (-1 + x)) 6 + -7x + x2 = ((-1 + 1x) + 2x * (-1 + x)) 6 + -7x + x2 = (-1 + 1x + (-1 * 2x + x * 2x)) 6 + -7x + x2 = (-1 + 1x + (-2x + 2x2)) Combine like terms: 1x + -2x = -1x 6 + -7x + x2 = (-1 + -1x + 2x2) Solving 6 + -7x + x2 = -1 + -1x + 2x2 Solving for variable 'x'. Reorder the terms: 6 + 1 + -7x + x + x2 + -2x2 = -1 + -1x + 2x2 + 1 + x + -2x2 Combine like terms: 6 + 1 = 7 7 + -7x + x + x2 + -2x2 = -1 + -1x + 2x2 + 1 + x + -2x2 Combine like terms: -7x + x = -6x 7 + -6x + x2 + -2x2 = -1 + -1x + 2x2 + 1 + x + -2x2 Combine like terms: x2 + -2x2 = -1x2 7 + -6x + -1x2 = -1 + -1x + 2x2 + 1 + x + -2x2 Reorder the terms: 7 + -6x + -1x2 = -1 + 1 + -1x + x + 2x2 + -2x2 Combine like terms: -1 + 1 = 0 7 + -6x + -1x2 = 0 + -1x + x + 2x2 + -2x2 7 + -6x + -1x2 = -1x + x + 2x2 + -2x2 Combine like terms: -1x + x = 0 7 + -6x + -1x2 = 0 + 2x2 + -2x2 7 + -6x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 7 + -6x + -1x2 = 0 Factor a trinomial. (1 + -1x)(7 + x) = 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 '(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 = -7Solution
x = {1, -7}
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