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Simplifying 0 = -12x2 + 1080x + -21600 Reorder the terms: 0 = -21600 + 1080x + -12x2 Solving 0 = -21600 + 1080x + -12x2 Solving for variable 'x'. Combine like terms: 0 + 21600 = 21600 21600 + -1080x + 12x2 = -21600 + 1080x + -12x2 + 21600 + -1080x + 12x2 Reorder the terms: 21600 + -1080x + 12x2 = -21600 + 21600 + 1080x + -1080x + -12x2 + 12x2 Combine like terms: -21600 + 21600 = 0 21600 + -1080x + 12x2 = 0 + 1080x + -1080x + -12x2 + 12x2 21600 + -1080x + 12x2 = 1080x + -1080x + -12x2 + 12x2 Combine like terms: 1080x + -1080x = 0 21600 + -1080x + 12x2 = 0 + -12x2 + 12x2 21600 + -1080x + 12x2 = -12x2 + 12x2 Combine like terms: -12x2 + 12x2 = 0 21600 + -1080x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(1800 + -90x + x2) = 0 Factor a trinomial. 12((30 + -1x)(60 + -1x)) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(30 + -1x)' equal to zero and attempt to solve: Simplifying 30 + -1x = 0 Solving 30 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + -1x = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -1x = 0 + -30 -1x = 0 + -30 Combine like terms: 0 + -30 = -30 -1x = -30 Divide each side by '-1'. x = 30 Simplifying x = 30Subproblem 2
Set the factor '(60 + -1x)' equal to zero and attempt to solve: Simplifying 60 + -1x = 0 Solving 60 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + -60 + -1x = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -1x = 0 + -60 -1x = 0 + -60 Combine like terms: 0 + -60 = -60 -1x = -60 Divide each side by '-1'. x = 60 Simplifying x = 60Solution
x = {30, 60}
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