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Simplifying 0 = x3 + -10x2 + 24x Reorder the terms: 0 = 24x + -10x2 + x3 Solving 0 = 24x + -10x2 + x3 Solving for variable 'x'. Remove the zero: -24x + 10x2 + -1x3 = 24x + -10x2 + x3 + -24x + 10x2 + -1x3 Reorder the terms: -24x + 10x2 + -1x3 = 24x + -24x + -10x2 + 10x2 + x3 + -1x3 Combine like terms: 24x + -24x = 0 -24x + 10x2 + -1x3 = 0 + -10x2 + 10x2 + x3 + -1x3 -24x + 10x2 + -1x3 = -10x2 + 10x2 + x3 + -1x3 Combine like terms: -10x2 + 10x2 = 0 -24x + 10x2 + -1x3 = 0 + x3 + -1x3 -24x + 10x2 + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 -24x + 10x2 + -1x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-24 + 10x + -1x2) = 0 Factor a trinomial. x((-6 + x)(4 + -1x)) = 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 '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {0, 6, 4}
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