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Simplifying -4x = 2x^{2}+ -6 Reorder the terms: -4x = -6 + 2x^{2}Solving -4x = -6 + 2x^{2}Solving for variable 'x'. Reorder the terms: 6 + -4x + -2x^{2}= -6 + 2x^{2}+ 6 + -2x^{2}Reorder the terms: 6 + -4x + -2x^{2}= -6 + 6 + 2x^{2}+ -2x^{2}Combine like terms: -6 + 6 = 0 6 + -4x + -2x^{2}= 0 + 2x^{2}+ -2x^{2}6 + -4x + -2x^{2}= 2x^{2}+ -2x^{2}Combine like terms: 2x^{2}+ -2x^{2}= 0 6 + -4x + -2x^{2}= 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -2x + -1x^{2}) = 0 Factor a trinomial. 2((1 + -1x)(3 + x)) = 0 Ignore the factor 2.## Subproblem 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 = 1## Subproblem 2

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3## Solution

x = {1, -3}

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