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Simplifying (x + -1)(3x + -1) + x(3x + -1) = 0 Reorder the terms: (-1 + x)(3x + -1) + x(3x + -1) = 0 Reorder the terms: (-1 + x)(-1 + 3x) + x(3x + -1) = 0 Multiply (-1 + x) * (-1 + 3x) (-1(-1 + 3x) + x(-1 + 3x)) + x(3x + -1) = 0 ((-1 * -1 + 3x * -1) + x(-1 + 3x)) + x(3x + -1) = 0 ((1 + -3x) + x(-1 + 3x)) + x(3x + -1) = 0 (1 + -3x + (-1 * x + 3x * x)) + x(3x + -1) = 0 (1 + -3x + (-1x + 3x2)) + x(3x + -1) = 0 Combine like terms: -3x + -1x = -4x (1 + -4x + 3x2) + x(3x + -1) = 0 Reorder the terms: 1 + -4x + 3x2 + x(-1 + 3x) = 0 1 + -4x + 3x2 + (-1 * x + 3x * x) = 0 1 + -4x + 3x2 + (-1x + 3x2) = 0 Reorder the terms: 1 + -4x + -1x + 3x2 + 3x2 = 0 Combine like terms: -4x + -1x = -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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