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Simplifying (3x + -1)(x + 1) + (3x + -1)(x + -2) = 0 Reorder the terms: (-1 + 3x)(x + 1) + (3x + -1)(x + -2) = 0 Reorder the terms: (-1 + 3x)(1 + x) + (3x + -1)(x + -2) = 0 Multiply (-1 + 3x) * (1 + x) (-1(1 + x) + 3x * (1 + x)) + (3x + -1)(x + -2) = 0 ((1 * -1 + x * -1) + 3x * (1 + x)) + (3x + -1)(x + -2) = 0 ((-1 + -1x) + 3x * (1 + x)) + (3x + -1)(x + -2) = 0 (-1 + -1x + (1 * 3x + x * 3x)) + (3x + -1)(x + -2) = 0 (-1 + -1x + (3x + 3x2)) + (3x + -1)(x + -2) = 0 Combine like terms: -1x + 3x = 2x (-1 + 2x + 3x2) + (3x + -1)(x + -2) = 0 Reorder the terms: -1 + 2x + 3x2 + (-1 + 3x)(x + -2) = 0 Reorder the terms: -1 + 2x + 3x2 + (-1 + 3x)(-2 + x) = 0 Multiply (-1 + 3x) * (-2 + x) -1 + 2x + 3x2 + (-1(-2 + x) + 3x * (-2 + x)) = 0 -1 + 2x + 3x2 + ((-2 * -1 + x * -1) + 3x * (-2 + x)) = 0 -1 + 2x + 3x2 + ((2 + -1x) + 3x * (-2 + x)) = 0 -1 + 2x + 3x2 + (2 + -1x + (-2 * 3x + x * 3x)) = 0 -1 + 2x + 3x2 + (2 + -1x + (-6x + 3x2)) = 0 Combine like terms: -1x + -6x = -7x -1 + 2x + 3x2 + (2 + -7x + 3x2) = 0 Reorder the terms: -1 + 2 + 2x + -7x + 3x2 + 3x2 = 0 Combine like terms: -1 + 2 = 1 1 + 2x + -7x + 3x2 + 3x2 = 0 Combine like terms: 2x + -7x = -5x 1 + -5x + 3x2 + 3x2 = 0 Combine like terms: 3x2 + 3x2 = 6x2 1 + -5x + 6x2 = 0 Solving 1 + -5x + 6x2 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -3x)(1 + -2x) = 0Subproblem 1
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 = 0.3333333333Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {0.3333333333, 0.5}
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