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Simplifying (3x + 2)(2x + -1) = 3 Reorder the terms: (2 + 3x)(2x + -1) = 3 Reorder the terms: (2 + 3x)(-1 + 2x) = 3 Multiply (2 + 3x) * (-1 + 2x) (2(-1 + 2x) + 3x * (-1 + 2x)) = 3 ((-1 * 2 + 2x * 2) + 3x * (-1 + 2x)) = 3 ((-2 + 4x) + 3x * (-1 + 2x)) = 3 (-2 + 4x + (-1 * 3x + 2x * 3x)) = 3 (-2 + 4x + (-3x + 6x2)) = 3 Combine like terms: 4x + -3x = 1x (-2 + 1x + 6x2) = 3 Solving -2 + 1x + 6x2 = 3 Solving for variable 'x'. Reorder the terms: -2 + -3 + 1x + 6x2 = 3 + -3 Combine like terms: -2 + -3 = -5 -5 + 1x + 6x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -5 + 1x + 6x2 = 0 Factor a trinomial. (-1 + -1x)(5 + -6x) = 0Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 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 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 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 = {-1, 0.8333333333}
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