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Simplifying 20m5 + -96m3 + 64m = 0 Reorder the terms: 64m + -96m3 + 20m5 = 0 Solving 64m + -96m3 + 20m5 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '4m'. 4m(16 + -24m2 + 5m4) = 0 Factor a trinomial. 4m((4 + -5m2)(4 + -1m2)) = 0 Factor a difference between two squares. 4m((4 + -5m2)((2 + m)(2 + -1m))) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'm' equal to zero and attempt to solve: Simplifying m = 0 Solving m = 0 Move all terms containing m to the left, all other terms to the right. Simplifying m = 0Subproblem 2
Set the factor '(4 + -5m2)' equal to zero and attempt to solve: Simplifying 4 + -5m2 = 0 Solving 4 + -5m2 = 0 Move all terms containing m to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5m2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5m2 = 0 + -4 -5m2 = 0 + -4 Combine like terms: 0 + -4 = -4 -5m2 = -4 Divide each side by '-5'. m2 = 0.8 Simplifying m2 = 0.8 Take the square root of each side: m = {-0.894427191, 0.894427191}Subproblem 3
Set the factor '(2 + m)' equal to zero and attempt to solve: Simplifying 2 + m = 0 Solving 2 + m = 0 Move all terms containing m to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + m = 0 + -2 Combine like terms: 2 + -2 = 0 0 + m = 0 + -2 m = 0 + -2 Combine like terms: 0 + -2 = -2 m = -2 Simplifying m = -2Subproblem 4
Set the factor '(2 + -1m)' equal to zero and attempt to solve: Simplifying 2 + -1m = 0 Solving 2 + -1m = 0 Move all terms containing m to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1m = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1m = 0 + -2 -1m = 0 + -2 Combine like terms: 0 + -2 = -2 -1m = -2 Divide each side by '-1'. m = 2 Simplifying m = 2Solution
m = {0, -0.894427191, 0.894427191, -2, 2}
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