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Simplifying x2 + -12x + -15x + -180 = 30x + -180 Reorder the terms: -180 + -12x + -15x + x2 = 30x + -180 Combine like terms: -12x + -15x = -27x -180 + -27x + x2 = 30x + -180 Reorder the terms: -180 + -27x + x2 = -180 + 30x Add '180' to each side of the equation. -180 + -27x + 180 + x2 = -180 + 180 + 30x Reorder the terms: -180 + 180 + -27x + x2 = -180 + 180 + 30x Combine like terms: -180 + 180 = 0 0 + -27x + x2 = -180 + 180 + 30x -27x + x2 = -180 + 180 + 30x Combine like terms: -180 + 180 = 0 -27x + x2 = 0 + 30x -27x + x2 = 30x Solving -27x + x2 = 30x Solving for variable 'x'. Reorder the terms: -27x + -30x + x2 = 30x + -30x Combine like terms: -27x + -30x = -57x -57x + x2 = 30x + -30x Combine like terms: 30x + -30x = 0 -57x + x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-57 + x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-57 + x)' equal to zero and attempt to solve: Simplifying -57 + x = 0 Solving -57 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '57' to each side of the equation. -57 + 57 + x = 0 + 57 Combine like terms: -57 + 57 = 0 0 + x = 0 + 57 x = 0 + 57 Combine like terms: 0 + 57 = 57 x = 57 Simplifying x = 57Solution
x = {0, 57}
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