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Simplifying 12x + -2x2 = 24 + -4x Solving 12x + -2x2 = 24 + -4x Solving for variable 'x'. Reorder the terms: -24 + 12x + 4x + -2x2 = 24 + -4x + -24 + 4x Combine like terms: 12x + 4x = 16x -24 + 16x + -2x2 = 24 + -4x + -24 + 4x Reorder the terms: -24 + 16x + -2x2 = 24 + -24 + -4x + 4x Combine like terms: 24 + -24 = 0 -24 + 16x + -2x2 = 0 + -4x + 4x -24 + 16x + -2x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -24 + 16x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 8x + -1x2) = 0 Factor a trinomial. 2((-6 + x)(2 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 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 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Subproblem 2
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 = 2Solution
x = {6, 2}
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