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Simplifying 0 = x(60 + -2x)(30 + -2x) Multiply (60 + -2x) * (30 + -2x) 0 = x(60(30 + -2x) + -2x * (30 + -2x)) 0 = x((30 * 60 + -2x * 60) + -2x * (30 + -2x)) 0 = x((1800 + -120x) + -2x * (30 + -2x)) 0 = x(1800 + -120x + (30 * -2x + -2x * -2x)) 0 = x(1800 + -120x + (-60x + 4x2)) Combine like terms: -120x + -60x = -180x 0 = x(1800 + -180x + 4x2) 0 = (1800 * x + -180x * x + 4x2 * x) 0 = (1800x + -180x2 + 4x3) Solving 0 = 1800x + -180x2 + 4x3 Solving for variable 'x'. Remove the zero: -1800x + 180x2 + -4x3 = 1800x + -180x2 + 4x3 + -1800x + 180x2 + -4x3 Reorder the terms: -1800x + 180x2 + -4x3 = 1800x + -1800x + -180x2 + 180x2 + 4x3 + -4x3 Combine like terms: 1800x + -1800x = 0 -1800x + 180x2 + -4x3 = 0 + -180x2 + 180x2 + 4x3 + -4x3 -1800x + 180x2 + -4x3 = -180x2 + 180x2 + 4x3 + -4x3 Combine like terms: -180x2 + 180x2 = 0 -1800x + 180x2 + -4x3 = 0 + 4x3 + -4x3 -1800x + 180x2 + -4x3 = 4x3 + -4x3 Combine like terms: 4x3 + -4x3 = 0 -1800x + 180x2 + -4x3 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(-450 + 45x + -1x2) = 0 Factor a trinomial. 4x((-30 + x)(15 + -1x)) = 0 Ignore the factor 4.Subproblem 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 '(-30 + x)' equal to zero and attempt to solve: Simplifying -30 + x = 0 Solving -30 + x = 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 + x = 0 + 30 Combine like terms: -30 + 30 = 0 0 + x = 0 + 30 x = 0 + 30 Combine like terms: 0 + 30 = 30 x = 30 Simplifying x = 30Subproblem 3
Set the factor '(15 + -1x)' equal to zero and attempt to solve: Simplifying 15 + -1x = 0 Solving 15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1x = 0 + -15 -1x = 0 + -15 Combine like terms: 0 + -15 = -15 -1x = -15 Divide each side by '-1'. x = 15 Simplifying x = 15Solution
x = {0, 30, 15}
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