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Simplifying -2x = 3x^{2}+ -1 Reorder the terms: -2x = -1 + 3x^{2}Solving -2x = -1 + 3x^{2}Solving for variable 'x'. Reorder the terms: 1 + -2x + -3x^{2}= -1 + 3x^{2}+ 1 + -3x^{2}Reorder the terms: 1 + -2x + -3x^{2}= -1 + 1 + 3x^{2}+ -3x^{2}Combine like terms: -1 + 1 = 0 1 + -2x + -3x^{2}= 0 + 3x^{2}+ -3x^{2}1 + -2x + -3x^{2}= 3x^{2}+ -3x^{2}Combine like terms: 3x^{2}+ -3x^{2}= 0 1 + -2x + -3x^{2}= 0 Factor a trinomial. (1 + -3x)(1 + x) = 0## Subproblem 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 = 0.3333333333## Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1## Solution

x = {0.3333333333, -1}

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