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Simplifying 0 = 12x2 + -276x + 1080 Reorder the terms: 0 = 1080 + -276x + 12x2 Solving 0 = 1080 + -276x + 12x2 Solving for variable 'x'. Combine like terms: 0 + -1080 = -1080 -1080 + 276x + -12x2 = 1080 + -276x + 12x2 + -1080 + 276x + -12x2 Reorder the terms: -1080 + 276x + -12x2 = 1080 + -1080 + -276x + 276x + 12x2 + -12x2 Combine like terms: 1080 + -1080 = 0 -1080 + 276x + -12x2 = 0 + -276x + 276x + 12x2 + -12x2 -1080 + 276x + -12x2 = -276x + 276x + 12x2 + -12x2 Combine like terms: -276x + 276x = 0 -1080 + 276x + -12x2 = 0 + 12x2 + -12x2 -1080 + 276x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -1080 + 276x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(-90 + 23x + -1x2) = 0 Factor a trinomial. 12((-18 + x)(5 + -1x)) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-18 + x)' equal to zero and attempt to solve: Simplifying -18 + x = 0 Solving -18 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 0 + 18 Combine like terms: -18 + 18 = 0 0 + x = 0 + 18 x = 0 + 18 Combine like terms: 0 + 18 = 18 x = 18 Simplifying x = 18Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {18, 5}
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