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Simplifying (2m2 + 2m + -3) + -1(4 + -3m + 5m2) + -1(2m + -1 + -6m2) = 0 Reorder the terms: (-3 + 2m + 2m2) + -1(4 + -3m + 5m2) + -1(2m + -1 + -6m2) = 0 Remove parenthesis around (-3 + 2m + 2m2) -3 + 2m + 2m2 + -1(4 + -3m + 5m2) + -1(2m + -1 + -6m2) = 0 -3 + 2m + 2m2 + (4 * -1 + -3m * -1 + 5m2 * -1) + -1(2m + -1 + -6m2) = 0 -3 + 2m + 2m2 + (-4 + 3m + -5m2) + -1(2m + -1 + -6m2) = 0 Reorder the terms: -3 + 2m + 2m2 + -4 + 3m + -5m2 + -1(-1 + 2m + -6m2) = 0 -3 + 2m + 2m2 + -4 + 3m + -5m2 + (-1 * -1 + 2m * -1 + -6m2 * -1) = 0 -3 + 2m + 2m2 + -4 + 3m + -5m2 + (1 + -2m + 6m2) = 0 Reorder the terms: -3 + -4 + 1 + 2m + 3m + -2m + 2m2 + -5m2 + 6m2 = 0 Combine like terms: -3 + -4 = -7 -7 + 1 + 2m + 3m + -2m + 2m2 + -5m2 + 6m2 = 0 Combine like terms: -7 + 1 = -6 -6 + 2m + 3m + -2m + 2m2 + -5m2 + 6m2 = 0 Combine like terms: 2m + 3m = 5m -6 + 5m + -2m + 2m2 + -5m2 + 6m2 = 0 Combine like terms: 5m + -2m = 3m -6 + 3m + 2m2 + -5m2 + 6m2 = 0 Combine like terms: 2m2 + -5m2 = -3m2 -6 + 3m + -3m2 + 6m2 = 0 Combine like terms: -3m2 + 6m2 = 3m2 -6 + 3m + 3m2 = 0 Solving -6 + 3m + 3m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + m + m2) = 0 Factor a trinomial. 3((-2 + -1m)(1 + -1m)) = 0 Ignore the factor 3.Subproblem 1
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 = -2Subproblem 2
Set the factor '(1 + -1m)' equal to zero and attempt to solve: Simplifying 1 + -1m = 0 Solving 1 + -1m = 0 Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1m = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1m = 0 + -1 -1m = 0 + -1 Combine like terms: 0 + -1 = -1 -1m = -1 Divide each side by '-1'. m = 1 Simplifying m = 1Solution
m = {-2, 1}
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