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Simplifying (4m + 7)(3m + -4) = -2m(4m + 13) + -19 Reorder the terms: (7 + 4m)(3m + -4) = -2m(4m + 13) + -19 Reorder the terms: (7 + 4m)(-4 + 3m) = -2m(4m + 13) + -19 Multiply (7 + 4m) * (-4 + 3m) (7(-4 + 3m) + 4m * (-4 + 3m)) = -2m(4m + 13) + -19 ((-4 * 7 + 3m * 7) + 4m * (-4 + 3m)) = -2m(4m + 13) + -19 ((-28 + 21m) + 4m * (-4 + 3m)) = -2m(4m + 13) + -19 (-28 + 21m + (-4 * 4m + 3m * 4m)) = -2m(4m + 13) + -19 (-28 + 21m + (-16m + 12m2)) = -2m(4m + 13) + -19 Combine like terms: 21m + -16m = 5m (-28 + 5m + 12m2) = -2m(4m + 13) + -19 Reorder the terms: -28 + 5m + 12m2 = -2m(13 + 4m) + -19 -28 + 5m + 12m2 = (13 * -2m + 4m * -2m) + -19 -28 + 5m + 12m2 = (-26m + -8m2) + -19 Reorder the terms: -28 + 5m + 12m2 = -19 + -26m + -8m2 Solving -28 + 5m + 12m2 = -19 + -26m + -8m2 Solving for variable 'm'. Reorder the terms: -28 + 19 + 5m + 26m + 12m2 + 8m2 = -19 + -26m + -8m2 + 19 + 26m + 8m2 Combine like terms: -28 + 19 = -9 -9 + 5m + 26m + 12m2 + 8m2 = -19 + -26m + -8m2 + 19 + 26m + 8m2 Combine like terms: 5m + 26m = 31m -9 + 31m + 12m2 + 8m2 = -19 + -26m + -8m2 + 19 + 26m + 8m2 Combine like terms: 12m2 + 8m2 = 20m2 -9 + 31m + 20m2 = -19 + -26m + -8m2 + 19 + 26m + 8m2 Reorder the terms: -9 + 31m + 20m2 = -19 + 19 + -26m + 26m + -8m2 + 8m2 Combine like terms: -19 + 19 = 0 -9 + 31m + 20m2 = 0 + -26m + 26m + -8m2 + 8m2 -9 + 31m + 20m2 = -26m + 26m + -8m2 + 8m2 Combine like terms: -26m + 26m = 0 -9 + 31m + 20m2 = 0 + -8m2 + 8m2 -9 + 31m + 20m2 = -8m2 + 8m2 Combine like terms: -8m2 + 8m2 = 0 -9 + 31m + 20m2 = 0 Factor a trinomial. (-9 + -5m)(1 + -4m) = 0Subproblem 1
Set the factor '(-9 + -5m)' equal to zero and attempt to solve: Simplifying -9 + -5m = 0 Solving -9 + -5m = 0 Move all terms containing m to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -5m = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -5m = 0 + 9 -5m = 0 + 9 Combine like terms: 0 + 9 = 9 -5m = 9 Divide each side by '-5'. m = -1.8 Simplifying m = -1.8Subproblem 2
Set the factor '(1 + -4m)' equal to zero and attempt to solve: Simplifying 1 + -4m = 0 Solving 1 + -4m = 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 + -4m = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4m = 0 + -1 -4m = 0 + -1 Combine like terms: 0 + -1 = -1 -4m = -1 Divide each side by '-4'. m = 0.25 Simplifying m = 0.25Solution
m = {-1.8, 0.25}
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