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Simplifying 3x2 + -5x + -213 = -2x2 + -3 Reorder the terms: -213 + -5x + 3x2 = -2x2 + -3 Reorder the terms: -213 + -5x + 3x2 = -3 + -2x2 Solving -213 + -5x + 3x2 = -3 + -2x2 Solving for variable 'x'. Reorder the terms: -213 + 3 + -5x + 3x2 + 2x2 = -3 + -2x2 + 3 + 2x2 Combine like terms: -213 + 3 = -210 -210 + -5x + 3x2 + 2x2 = -3 + -2x2 + 3 + 2x2 Combine like terms: 3x2 + 2x2 = 5x2 -210 + -5x + 5x2 = -3 + -2x2 + 3 + 2x2 Reorder the terms: -210 + -5x + 5x2 = -3 + 3 + -2x2 + 2x2 Combine like terms: -3 + 3 = 0 -210 + -5x + 5x2 = 0 + -2x2 + 2x2 -210 + -5x + 5x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -210 + -5x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-42 + -1x + x2) = 0 Factor a trinomial. 5((-6 + -1x)(7 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {-6, 7}
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