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Simplifying (x + -6)(x + 1) + -1(2 + -1x)(x + 3) = 36 Reorder the terms: (-6 + x)(x + 1) + -1(2 + -1x)(x + 3) = 36 Reorder the terms: (-6 + x)(1 + x) + -1(2 + -1x)(x + 3) = 36 Multiply (-6 + x) * (1 + x) (-6(1 + x) + x(1 + x)) + -1(2 + -1x)(x + 3) = 36 ((1 * -6 + x * -6) + x(1 + x)) + -1(2 + -1x)(x + 3) = 36 ((-6 + -6x) + x(1 + x)) + -1(2 + -1x)(x + 3) = 36 (-6 + -6x + (1 * x + x * x)) + -1(2 + -1x)(x + 3) = 36 (-6 + -6x + (1x + x2)) + -1(2 + -1x)(x + 3) = 36 Combine like terms: -6x + 1x = -5x (-6 + -5x + x2) + -1(2 + -1x)(x + 3) = 36 Reorder the terms: -6 + -5x + x2 + -1(2 + -1x)(3 + x) = 36 Multiply (2 + -1x) * (3 + x) -6 + -5x + x2 + -1(2(3 + x) + -1x * (3 + x)) = 36 -6 + -5x + x2 + -1((3 * 2 + x * 2) + -1x * (3 + x)) = 36 -6 + -5x + x2 + -1((6 + 2x) + -1x * (3 + x)) = 36 -6 + -5x + x2 + -1(6 + 2x + (3 * -1x + x * -1x)) = 36 -6 + -5x + x2 + -1(6 + 2x + (-3x + -1x2)) = 36 Combine like terms: 2x + -3x = -1x -6 + -5x + x2 + -1(6 + -1x + -1x2) = 36 -6 + -5x + x2 + (6 * -1 + -1x * -1 + -1x2 * -1) = 36 -6 + -5x + x2 + (-6 + 1x + 1x2) = 36 Reorder the terms: -6 + -6 + -5x + 1x + x2 + 1x2 = 36 Combine like terms: -6 + -6 = -12 -12 + -5x + 1x + x2 + 1x2 = 36 Combine like terms: -5x + 1x = -4x -12 + -4x + x2 + 1x2 = 36 Combine like terms: x2 + 1x2 = 2x2 -12 + -4x + 2x2 = 36 Solving -12 + -4x + 2x2 = 36 Solving for variable 'x'. Reorder the terms: -12 + -36 + -4x + 2x2 = 36 + -36 Combine like terms: -12 + -36 = -48 -48 + -4x + 2x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -48 + -4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-24 + -2x + x2) = 0 Factor a trinomial. 2((-4 + -1x)(6 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 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 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 2
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 = 6Solution
x = {-4, 6}
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