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Simplifying (2x + -1)(3x + -2) = 0 Reorder the terms: (-1 + 2x)(3x + -2) = 0 Reorder the terms: (-1 + 2x)(-2 + 3x) = 0 Multiply (-1 + 2x) * (-2 + 3x) (-1(-2 + 3x) + 2x * (-2 + 3x)) = 0 ((-2 * -1 + 3x * -1) + 2x * (-2 + 3x)) = 0 ((2 + -3x) + 2x * (-2 + 3x)) = 0 (2 + -3x + (-2 * 2x + 3x * 2x)) = 0 (2 + -3x + (-4x + 6x2)) = 0 Combine like terms: -3x + -4x = -7x (2 + -7x + 6x2) = 0 Solving 2 + -7x + 6x2 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -2x)(2 + -3x) = 0Subproblem 1
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 = 0.5Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {0.5, 0.6666666667}
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