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Simplifying 0 = 12x2 + 72x + -84 Reorder the terms: 0 = -84 + 72x + 12x2 Solving 0 = -84 + 72x + 12x2 Solving for variable 'x'. Combine like terms: 0 + 84 = 84 84 + -72x + -12x2 = -84 + 72x + 12x2 + 84 + -72x + -12x2 Reorder the terms: 84 + -72x + -12x2 = -84 + 84 + 72x + -72x + 12x2 + -12x2 Combine like terms: -84 + 84 = 0 84 + -72x + -12x2 = 0 + 72x + -72x + 12x2 + -12x2 84 + -72x + -12x2 = 72x + -72x + 12x2 + -12x2 Combine like terms: 72x + -72x = 0 84 + -72x + -12x2 = 0 + 12x2 + -12x2 84 + -72x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 84 + -72x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(7 + -6x + -1x2) = 0 Factor a trinomial. 12((1 + -1x)(7 + x)) = 0 Ignore the factor 12.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 = 1Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 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 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Solution
x = {1, -7}
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