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Simplifying 2m(7m + -6)(m + 5) = 0 Reorder the terms: 2m(-6 + 7m)(m + 5) = 0 Reorder the terms: 2m(-6 + 7m)(5 + m) = 0 Multiply (-6 + 7m) * (5 + m) 2m(-6(5 + m) + 7m * (5 + m)) = 0 2m((5 * -6 + m * -6) + 7m * (5 + m)) = 0 2m((-30 + -6m) + 7m * (5 + m)) = 0 2m(-30 + -6m + (5 * 7m + m * 7m)) = 0 2m(-30 + -6m + (35m + 7m2)) = 0 Combine like terms: -6m + 35m = 29m 2m(-30 + 29m + 7m2) = 0 (-30 * 2m + 29m * 2m + 7m2 * 2m) = 0 (-60m + 58m2 + 14m3) = 0 Solving -60m + 58m2 + 14m3 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2m'. 2m(-30 + 29m + 7m2) = 0 Factor a trinomial. 2m((-5 + -1m)(6 + -7m)) = 0 Ignore the factor 2.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 '(-5 + -1m)' equal to zero and attempt to solve: Simplifying -5 + -1m = 0 Solving -5 + -1m = 0 Move all terms containing m to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1m = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1m = 0 + 5 -1m = 0 + 5 Combine like terms: 0 + 5 = 5 -1m = 5 Divide each side by '-1'. m = -5 Simplifying m = -5Subproblem 3
Set the factor '(6 + -7m)' equal to zero and attempt to solve: Simplifying 6 + -7m = 0 Solving 6 + -7m = 0 Move all terms containing m to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -7m = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7m = 0 + -6 -7m = 0 + -6 Combine like terms: 0 + -6 = -6 -7m = -6 Divide each side by '-7'. m = 0.8571428571 Simplifying m = 0.8571428571Solution
m = {0, -5, 0.8571428571}
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