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Simplifying (x + 6)(x + -6) = (2x + 1)(x + -6) Reorder the terms: (6 + x)(x + -6) = (2x + 1)(x + -6) Reorder the terms: (6 + x)(-6 + x) = (2x + 1)(x + -6) Multiply (6 + x) * (-6 + x) (6(-6 + x) + x(-6 + x)) = (2x + 1)(x + -6) ((-6 * 6 + x * 6) + x(-6 + x)) = (2x + 1)(x + -6) ((-36 + 6x) + x(-6 + x)) = (2x + 1)(x + -6) (-36 + 6x + (-6 * x + x * x)) = (2x + 1)(x + -6) (-36 + 6x + (-6x + x2)) = (2x + 1)(x + -6) Combine like terms: 6x + -6x = 0 (-36 + 0 + x2) = (2x + 1)(x + -6) (-36 + x2) = (2x + 1)(x + -6) Reorder the terms: -36 + x2 = (1 + 2x)(x + -6) Reorder the terms: -36 + x2 = (1 + 2x)(-6 + x) Multiply (1 + 2x) * (-6 + x) -36 + x2 = (1(-6 + x) + 2x * (-6 + x)) -36 + x2 = ((-6 * 1 + x * 1) + 2x * (-6 + x)) -36 + x2 = ((-6 + 1x) + 2x * (-6 + x)) -36 + x2 = (-6 + 1x + (-6 * 2x + x * 2x)) -36 + x2 = (-6 + 1x + (-12x + 2x2)) Combine like terms: 1x + -12x = -11x -36 + x2 = (-6 + -11x + 2x2) Solving -36 + x2 = -6 + -11x + 2x2 Solving for variable 'x'. Reorder the terms: -36 + 6 + 11x + x2 + -2x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2 Combine like terms: -36 + 6 = -30 -30 + 11x + x2 + -2x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -30 + 11x + -1x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2 Reorder the terms: -30 + 11x + -1x2 = -6 + 6 + -11x + 11x + 2x2 + -2x2 Combine like terms: -6 + 6 = 0 -30 + 11x + -1x2 = 0 + -11x + 11x + 2x2 + -2x2 -30 + 11x + -1x2 = -11x + 11x + 2x2 + -2x2 Combine like terms: -11x + 11x = 0 -30 + 11x + -1x2 = 0 + 2x2 + -2x2 -30 + 11x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -30 + 11x + -1x2 = 0 Factor a trinomial. (-6 + x)(5 + -1x) = 0Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 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 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {6, 5}
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