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Simplifying (x + -6)(x + -5) = 2x + -12 Reorder the terms: (-6 + x)(x + -5) = 2x + -12 Reorder the terms: (-6 + x)(-5 + x) = 2x + -12 Multiply (-6 + x) * (-5 + x) (-6(-5 + x) + x(-5 + x)) = 2x + -12 ((-5 * -6 + x * -6) + x(-5 + x)) = 2x + -12 ((30 + -6x) + x(-5 + x)) = 2x + -12 (30 + -6x + (-5 * x + x * x)) = 2x + -12 (30 + -6x + (-5x + x2)) = 2x + -12 Combine like terms: -6x + -5x = -11x (30 + -11x + x2) = 2x + -12 Reorder the terms: 30 + -11x + x2 = -12 + 2x Solving 30 + -11x + x2 = -12 + 2x Solving for variable 'x'. Reorder the terms: 30 + 12 + -11x + -2x + x2 = -12 + 2x + 12 + -2x Combine like terms: 30 + 12 = 42 42 + -11x + -2x + x2 = -12 + 2x + 12 + -2x Combine like terms: -11x + -2x = -13x 42 + -13x + x2 = -12 + 2x + 12 + -2x Reorder the terms: 42 + -13x + x2 = -12 + 12 + 2x + -2x Combine like terms: -12 + 12 = 0 42 + -13x + x2 = 0 + 2x + -2x 42 + -13x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 42 + -13x + x2 = 0 Factor a trinomial. (6 + -1x)(7 + -1x) = 0Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {6, 7}
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