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Simplifying 42 + -12x = 3x2 + 6 Reorder the terms: 42 + -12x = 6 + 3x2 Solving 42 + -12x = 6 + 3x2 Solving for variable 'x'. Reorder the terms: 42 + -6 + -12x + -3x2 = 6 + 3x2 + -6 + -3x2 Combine like terms: 42 + -6 = 36 36 + -12x + -3x2 = 6 + 3x2 + -6 + -3x2 Reorder the terms: 36 + -12x + -3x2 = 6 + -6 + 3x2 + -3x2 Combine like terms: 6 + -6 = 0 36 + -12x + -3x2 = 0 + 3x2 + -3x2 36 + -12x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 36 + -12x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(12 + -4x + -1x2) = 0 Factor a trinomial. 3((2 + -1x)(6 + x)) = 0 Ignore the factor 3.Subproblem 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 '(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 = -6Solution
x = {2, -6}
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