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Simplifying x(75 + -5x) = 180 (75 * x + -5x * x) = 180 (75x + -5x2) = 180 Solving 75x + -5x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 75x + -5x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 75x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-36 + 15x + -1x2) = 0 Factor a trinomial. 5((-12 + x)(3 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-12 + x)' equal to zero and attempt to solve: Simplifying -12 + x = 0 Solving -12 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + x = 0 + 12 x = 0 + 12 Combine like terms: 0 + 12 = 12 x = 12 Simplifying x = 12Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {12, 3}
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