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Simplifying 0 = -3x2 + 138x + -1080 Reorder the terms: 0 = -1080 + 138x + -3x2 Solving 0 = -1080 + 138x + -3x2 Solving for variable 'x'. Combine like terms: 0 + 1080 = 1080 1080 + -138x + 3x2 = -1080 + 138x + -3x2 + 1080 + -138x + 3x2 Reorder the terms: 1080 + -138x + 3x2 = -1080 + 1080 + 138x + -138x + -3x2 + 3x2 Combine like terms: -1080 + 1080 = 0 1080 + -138x + 3x2 = 0 + 138x + -138x + -3x2 + 3x2 1080 + -138x + 3x2 = 138x + -138x + -3x2 + 3x2 Combine like terms: 138x + -138x = 0 1080 + -138x + 3x2 = 0 + -3x2 + 3x2 1080 + -138x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 1080 + -138x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(360 + -46x + x2) = 0 Factor a trinomial. 3((10 + -1x)(36 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Subproblem 2
Set the factor '(36 + -1x)' equal to zero and attempt to solve: Simplifying 36 + -1x = 0 Solving 36 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -36 + -1x = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -1x = 0 + -36 -1x = 0 + -36 Combine like terms: 0 + -36 = -36 -1x = -36 Divide each side by '-1'. x = 36 Simplifying x = 36Solution
x = {10, 36}
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