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Simplifying 45m2 + 120m + -100 = 0 Reorder the terms: -100 + 120m + 45m2 = 0 Solving -100 + 120m + 45m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '5'. 5(-20 + 24m + 9m2) = 0 Factor a trinomial. 5((-10 + -3m)(2 + -3m)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-10 + -3m)' equal to zero and attempt to solve: Simplifying -10 + -3m = 0 Solving -10 + -3m = 0 Move all terms containing m to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -3m = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -3m = 0 + 10 -3m = 0 + 10 Combine like terms: 0 + 10 = 10 -3m = 10 Divide each side by '-3'. m = -3.333333333 Simplifying m = -3.333333333Subproblem 2
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 = {-3.333333333, 0.6666666667}
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