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Simplifying (3x + 5)(x + -6) = 8 Reorder the terms: (5 + 3x)(x + -6) = 8 Reorder the terms: (5 + 3x)(-6 + x) = 8 Multiply (5 + 3x) * (-6 + x) (5(-6 + x) + 3x * (-6 + x)) = 8 ((-6 * 5 + x * 5) + 3x * (-6 + x)) = 8 ((-30 + 5x) + 3x * (-6 + x)) = 8 (-30 + 5x + (-6 * 3x + x * 3x)) = 8 (-30 + 5x + (-18x + 3x2)) = 8 Combine like terms: 5x + -18x = -13x (-30 + -13x + 3x2) = 8 Solving -30 + -13x + 3x2 = 8 Solving for variable 'x'. Reorder the terms: -30 + -8 + -13x + 3x2 = 8 + -8 Combine like terms: -30 + -8 = -38 -38 + -13x + 3x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -38 + -13x + 3x2 = 0 Factor a trinomial. (-2 + -1x)(19 + -3x) = 0Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
Set the factor '(19 + -3x)' equal to zero and attempt to solve: Simplifying 19 + -3x = 0 Solving 19 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + -3x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -3x = 0 + -19 -3x = 0 + -19 Combine like terms: 0 + -19 = -19 -3x = -19 Divide each side by '-3'. x = 6.333333333 Simplifying x = 6.333333333Solution
x = {-2, 6.333333333}
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