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Simplifying (2x + -1)(3x + -1) = 1 Reorder the terms: (-1 + 2x)(3x + -1) = 1 Reorder the terms: (-1 + 2x)(-1 + 3x) = 1 Multiply (-1 + 2x) * (-1 + 3x) (-1(-1 + 3x) + 2x * (-1 + 3x)) = 1 ((-1 * -1 + 3x * -1) + 2x * (-1 + 3x)) = 1 ((1 + -3x) + 2x * (-1 + 3x)) = 1 (1 + -3x + (-1 * 2x + 3x * 2x)) = 1 (1 + -3x + (-2x + 6x2)) = 1 Combine like terms: -3x + -2x = -5x (1 + -5x + 6x2) = 1 Add '-1' to each side of the equation. 1 + -5x + -1 + 6x2 = 1 + -1 Reorder the terms: 1 + -1 + -5x + 6x2 = 1 + -1 Combine like terms: 1 + -1 = 0 0 + -5x + 6x2 = 1 + -1 -5x + 6x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -5x + 6x2 = 0 Solving -5x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-5 + 6x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-5 + 6x)' equal to zero and attempt to solve: Simplifying -5 + 6x = 0 Solving -5 + 6x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 6x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 6x = 0 + 5 6x = 0 + 5 Combine like terms: 0 + 5 = 5 6x = 5 Divide each side by '6'. x = 0.8333333333 Simplifying x = 0.8333333333Solution
x = {0, 0.8333333333}
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