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