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Simplifying 0 = 4x3 + 10x2 + -24x Reorder the terms: 0 = -24x + 10x2 + 4x3 Solving 0 = -24x + 10x2 + 4x3 Solving for variable 'x'. Remove the zero: 24x + -10x2 + -4x3 = -24x + 10x2 + 4x3 + 24x + -10x2 + -4x3 Reorder the terms: 24x + -10x2 + -4x3 = -24x + 24x + 10x2 + -10x2 + 4x3 + -4x3 Combine like terms: -24x + 24x = 0 24x + -10x2 + -4x3 = 0 + 10x2 + -10x2 + 4x3 + -4x3 24x + -10x2 + -4x3 = 10x2 + -10x2 + 4x3 + -4x3 Combine like terms: 10x2 + -10x2 = 0 24x + -10x2 + -4x3 = 0 + 4x3 + -4x3 24x + -10x2 + -4x3 = 4x3 + -4x3 Combine like terms: 4x3 + -4x3 = 0 24x + -10x2 + -4x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(12 + -5x + -2x2) = 0 Factor a trinomial. 2x((3 + -2x)(4 + x)) = 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 '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Subproblem 3
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {0, 1.5, -4}
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