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Simplifying 12(10m + 8)(6m + 4)(2m) = 0 Reorder the terms: 12(8 + 10m)(6m + 4)(2m) = 0 Reorder the terms: 12(8 + 10m)(4 + 6m)(2m) = 0 Remove parenthesis around (2m) 12(8 + 10m)(4 + 6m) * 2m = 0 Reorder the terms for easier multiplication: 12 * 2m(8 + 10m)(4 + 6m) = 0 Multiply 12 * 2 24m(8 + 10m)(4 + 6m) = 0 Multiply (8 + 10m) * (4 + 6m) 24m(8(4 + 6m) + 10m * (4 + 6m)) = 0 24m((4 * 8 + 6m * 8) + 10m * (4 + 6m)) = 0 24m((32 + 48m) + 10m * (4 + 6m)) = 0 24m(32 + 48m + (4 * 10m + 6m * 10m)) = 0 24m(32 + 48m + (40m + 60m2)) = 0 Combine like terms: 48m + 40m = 88m 24m(32 + 88m + 60m2) = 0 (32 * 24m + 88m * 24m + 60m2 * 24m) = 0 (768m + 2112m2 + 1440m3) = 0 Solving 768m + 2112m2 + 1440m3 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '96m'. 96m(8 + 22m + 15m2) = 0 Factor a trinomial. 96m((4 + 5m)(2 + 3m)) = 0 Ignore the factor 96.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 + 5m)' equal to zero and attempt to solve: Simplifying 4 + 5m = 0 Solving 4 + 5m = 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 + 5m = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5m = 0 + -4 5m = 0 + -4 Combine like terms: 0 + -4 = -4 5m = -4 Divide each side by '5'. m = -0.8 Simplifying m = -0.8Subproblem 3
Set the factor '(2 + 3m)' equal to zero and attempt to solve: Simplifying 2 + 3m = 0 Solving 2 + 3m = 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 + 3m = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3m = 0 + -2 3m = 0 + -2 Combine like terms: 0 + -2 = -2 3m = -2 Divide each side by '3'. m = -0.6666666667 Simplifying m = -0.6666666667Solution
m = {0, -0.8, -0.6666666667}
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