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Simplifying (3x + -1)(x + 8) + (3x + -1)(x + 1) = 0 Reorder the terms: (-1 + 3x)(x + 8) + (3x + -1)(x + 1) = 0 Reorder the terms: (-1 + 3x)(8 + x) + (3x + -1)(x + 1) = 0 Multiply (-1 + 3x) * (8 + x) (-1(8 + x) + 3x * (8 + x)) + (3x + -1)(x + 1) = 0 ((8 * -1 + x * -1) + 3x * (8 + x)) + (3x + -1)(x + 1) = 0 ((-8 + -1x) + 3x * (8 + x)) + (3x + -1)(x + 1) = 0 (-8 + -1x + (8 * 3x + x * 3x)) + (3x + -1)(x + 1) = 0 (-8 + -1x + (24x + 3x2)) + (3x + -1)(x + 1) = 0 Combine like terms: -1x + 24x = 23x (-8 + 23x + 3x2) + (3x + -1)(x + 1) = 0 Reorder the terms: -8 + 23x + 3x2 + (-1 + 3x)(x + 1) = 0 Reorder the terms: -8 + 23x + 3x2 + (-1 + 3x)(1 + x) = 0 Multiply (-1 + 3x) * (1 + x) -8 + 23x + 3x2 + (-1(1 + x) + 3x * (1 + x)) = 0 -8 + 23x + 3x2 + ((1 * -1 + x * -1) + 3x * (1 + x)) = 0 -8 + 23x + 3x2 + ((-1 + -1x) + 3x * (1 + x)) = 0 -8 + 23x + 3x2 + (-1 + -1x + (1 * 3x + x * 3x)) = 0 -8 + 23x + 3x2 + (-1 + -1x + (3x + 3x2)) = 0 Combine like terms: -1x + 3x = 2x -8 + 23x + 3x2 + (-1 + 2x + 3x2) = 0 Reorder the terms: -8 + -1 + 23x + 2x + 3x2 + 3x2 = 0 Combine like terms: -8 + -1 = -9 -9 + 23x + 2x + 3x2 + 3x2 = 0 Combine like terms: 23x + 2x = 25x -9 + 25x + 3x2 + 3x2 = 0 Combine like terms: 3x2 + 3x2 = 6x2 -9 + 25x + 6x2 = 0 Solving -9 + 25x + 6x2 = 0 Solving for variable 'x'. Factor a trinomial. (-9 + -2x)(1 + -3x) = 0Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve: Simplifying -9 + -2x = 0 Solving -9 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2x = 0 + 9 -2x = 0 + 9 Combine like terms: 0 + 9 = 9 -2x = 9 Divide each side by '-2'. x = -4.5 Simplifying x = -4.5Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {-4.5, 0.3333333333}
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