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Simplifying 0 = x(45 + -2x)(24 + -2x) Multiply (45 + -2x) * (24 + -2x) 0 = x(45(24 + -2x) + -2x * (24 + -2x)) 0 = x((24 * 45 + -2x * 45) + -2x * (24 + -2x)) 0 = x((1080 + -90x) + -2x * (24 + -2x)) 0 = x(1080 + -90x + (24 * -2x + -2x * -2x)) 0 = x(1080 + -90x + (-48x + 4x2)) Combine like terms: -90x + -48x = -138x 0 = x(1080 + -138x + 4x2) 0 = (1080 * x + -138x * x + 4x2 * x) 0 = (1080x + -138x2 + 4x3) Solving 0 = 1080x + -138x2 + 4x3 Solving for variable 'x'. Remove the zero: -1080x + 138x2 + -4x3 = 1080x + -138x2 + 4x3 + -1080x + 138x2 + -4x3 Reorder the terms: -1080x + 138x2 + -4x3 = 1080x + -1080x + -138x2 + 138x2 + 4x3 + -4x3 Combine like terms: 1080x + -1080x = 0 -1080x + 138x2 + -4x3 = 0 + -138x2 + 138x2 + 4x3 + -4x3 -1080x + 138x2 + -4x3 = -138x2 + 138x2 + 4x3 + -4x3 Combine like terms: -138x2 + 138x2 = 0 -1080x + 138x2 + -4x3 = 0 + 4x3 + -4x3 -1080x + 138x2 + -4x3 = 4x3 + -4x3 Combine like terms: 4x3 + -4x3 = 0 -1080x + 138x2 + -4x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(-540 + 69x + -2x2) = 0 Factor a trinomial. 2x((-45 + 2x)(12 + -1x)) = 0 Ignore the factor 2.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 '(-45 + 2x)' equal to zero and attempt to solve: Simplifying -45 + 2x = 0 Solving -45 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + 2x = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 2x = 0 + 45 2x = 0 + 45 Combine like terms: 0 + 45 = 45 2x = 45 Divide each side by '2'. x = 22.5 Simplifying x = 22.5Subproblem 3
Set the factor '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 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 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12Solution
x = {0, 22.5, 12}
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