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Simplifying (3x + -1)(x + 1) + -1(1 + -3x)(2x + 7) = 0 Reorder the terms: (-1 + 3x)(x + 1) + -1(1 + -3x)(2x + 7) = 0 Reorder the terms: (-1 + 3x)(1 + x) + -1(1 + -3x)(2x + 7) = 0 Multiply (-1 + 3x) * (1 + x) (-1(1 + x) + 3x * (1 + x)) + -1(1 + -3x)(2x + 7) = 0 ((1 * -1 + x * -1) + 3x * (1 + x)) + -1(1 + -3x)(2x + 7) = 0 ((-1 + -1x) + 3x * (1 + x)) + -1(1 + -3x)(2x + 7) = 0 (-1 + -1x + (1 * 3x + x * 3x)) + -1(1 + -3x)(2x + 7) = 0 (-1 + -1x + (3x + 3x2)) + -1(1 + -3x)(2x + 7) = 0 Combine like terms: -1x + 3x = 2x (-1 + 2x + 3x2) + -1(1 + -3x)(2x + 7) = 0 Reorder the terms: -1 + 2x + 3x2 + -1(1 + -3x)(7 + 2x) = 0 Multiply (1 + -3x) * (7 + 2x) -1 + 2x + 3x2 + -1(1(7 + 2x) + -3x * (7 + 2x)) = 0 -1 + 2x + 3x2 + -1((7 * 1 + 2x * 1) + -3x * (7 + 2x)) = 0 -1 + 2x + 3x2 + -1((7 + 2x) + -3x * (7 + 2x)) = 0 -1 + 2x + 3x2 + -1(7 + 2x + (7 * -3x + 2x * -3x)) = 0 -1 + 2x + 3x2 + -1(7 + 2x + (-21x + -6x2)) = 0 Combine like terms: 2x + -21x = -19x -1 + 2x + 3x2 + -1(7 + -19x + -6x2) = 0 -1 + 2x + 3x2 + (7 * -1 + -19x * -1 + -6x2 * -1) = 0 -1 + 2x + 3x2 + (-7 + 19x + 6x2) = 0 Reorder the terms: -1 + -7 + 2x + 19x + 3x2 + 6x2 = 0 Combine like terms: -1 + -7 = -8 -8 + 2x + 19x + 3x2 + 6x2 = 0 Combine like terms: 2x + 19x = 21x -8 + 21x + 3x2 + 6x2 = 0 Combine like terms: 3x2 + 6x2 = 9x2 -8 + 21x + 9x2 = 0 Solving -8 + 21x + 9x2 = 0 Solving for variable 'x'. Factor a trinomial. (-8 + -3x)(1 + -3x) = 0Subproblem 1
Set the factor '(-8 + -3x)' equal to zero and attempt to solve: Simplifying -8 + -3x = 0 Solving -8 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -3x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3x = 0 + 8 -3x = 0 + 8 Combine like terms: 0 + 8 = 8 -3x = 8 Divide each side by '-3'. x = -2.666666667 Simplifying x = -2.666666667Subproblem 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 = {-2.666666667, 0.3333333333}
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