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Simplifying (m + -1)(3m + 7) = 3(m + 5) + -12 Reorder the terms: (-1 + m)(3m + 7) = 3(m + 5) + -12 Reorder the terms: (-1 + m)(7 + 3m) = 3(m + 5) + -12 Multiply (-1 + m) * (7 + 3m) (-1(7 + 3m) + m(7 + 3m)) = 3(m + 5) + -12 ((7 * -1 + 3m * -1) + m(7 + 3m)) = 3(m + 5) + -12 ((-7 + -3m) + m(7 + 3m)) = 3(m + 5) + -12 (-7 + -3m + (7 * m + 3m * m)) = 3(m + 5) + -12 (-7 + -3m + (7m + 3m2)) = 3(m + 5) + -12 Combine like terms: -3m + 7m = 4m (-7 + 4m + 3m2) = 3(m + 5) + -12 Reorder the terms: -7 + 4m + 3m2 = 3(5 + m) + -12 -7 + 4m + 3m2 = (5 * 3 + m * 3) + -12 -7 + 4m + 3m2 = (15 + 3m) + -12 Reorder the terms: -7 + 4m + 3m2 = 15 + -12 + 3m Combine like terms: 15 + -12 = 3 -7 + 4m + 3m2 = 3 + 3m Solving -7 + 4m + 3m2 = 3 + 3m Solving for variable 'm'. Reorder the terms: -7 + -3 + 4m + -3m + 3m2 = 3 + 3m + -3 + -3m Combine like terms: -7 + -3 = -10 -10 + 4m + -3m + 3m2 = 3 + 3m + -3 + -3m Combine like terms: 4m + -3m = 1m -10 + 1m + 3m2 = 3 + 3m + -3 + -3m Reorder the terms: -10 + 1m + 3m2 = 3 + -3 + 3m + -3m Combine like terms: 3 + -3 = 0 -10 + 1m + 3m2 = 0 + 3m + -3m -10 + 1m + 3m2 = 3m + -3m Combine like terms: 3m + -3m = 0 -10 + 1m + 3m2 = 0 Factor a trinomial. (-2 + -1m)(5 + -3m) = 0Subproblem 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 '(5 + -3m)' equal to zero and attempt to solve: Simplifying 5 + -3m = 0 Solving 5 + -3m = 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 + -3m = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3m = 0 + -5 -3m = 0 + -5 Combine like terms: 0 + -5 = -5 -3m = -5 Divide each side by '-3'. m = 1.666666667 Simplifying m = 1.666666667Solution
m = {-2, 1.666666667}
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