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Simplifying 0 = 3x3 + -24x2 + 45x Reorder the terms: 0 = 45x + -24x2 + 3x3 Solving 0 = 45x + -24x2 + 3x3 Solving for variable 'x'. Remove the zero: -45x + 24x2 + -3x3 = 45x + -24x2 + 3x3 + -45x + 24x2 + -3x3 Reorder the terms: -45x + 24x2 + -3x3 = 45x + -45x + -24x2 + 24x2 + 3x3 + -3x3 Combine like terms: 45x + -45x = 0 -45x + 24x2 + -3x3 = 0 + -24x2 + 24x2 + 3x3 + -3x3 -45x + 24x2 + -3x3 = -24x2 + 24x2 + 3x3 + -3x3 Combine like terms: -24x2 + 24x2 = 0 -45x + 24x2 + -3x3 = 0 + 3x3 + -3x3 -45x + 24x2 + -3x3 = 3x3 + -3x3 Combine like terms: 3x3 + -3x3 = 0 -45x + 24x2 + -3x3 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(-15 + 8x + -1x2) = 0 Factor a trinomial. 3x((-5 + x)(3 + -1x)) = 0 Ignore the factor 3.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 '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Subproblem 3
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 = {0, 5, 3}
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