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Simplifying (m2 + 3m + 2)(2m2 + -6m + 4) = 0 Reorder the terms: (2 + 3m + m2)(2m2 + -6m + 4) = 0 Reorder the terms: (2 + 3m + m2)(4 + -6m + 2m2) = 0 Multiply (2 + 3m + m2) * (4 + -6m + 2m2) (2(4 + -6m + 2m2) + 3m * (4 + -6m + 2m2) + m2(4 + -6m + 2m2)) = 0 ((4 * 2 + -6m * 2 + 2m2 * 2) + 3m * (4 + -6m + 2m2) + m2(4 + -6m + 2m2)) = 0 ((8 + -12m + 4m2) + 3m * (4 + -6m + 2m2) + m2(4 + -6m + 2m2)) = 0 (8 + -12m + 4m2 + (4 * 3m + -6m * 3m + 2m2 * 3m) + m2(4 + -6m + 2m2)) = 0 (8 + -12m + 4m2 + (12m + -18m2 + 6m3) + m2(4 + -6m + 2m2)) = 0 (8 + -12m + 4m2 + 12m + -18m2 + 6m3 + (4 * m2 + -6m * m2 + 2m2 * m2)) = 0 (8 + -12m + 4m2 + 12m + -18m2 + 6m3 + (4m2 + -6m3 + 2m4)) = 0 Reorder the terms: (8 + -12m + 12m + 4m2 + -18m2 + 4m2 + 6m3 + -6m3 + 2m4) = 0 Combine like terms: -12m + 12m = 0 (8 + 0 + 4m2 + -18m2 + 4m2 + 6m3 + -6m3 + 2m4) = 0 (8 + 4m2 + -18m2 + 4m2 + 6m3 + -6m3 + 2m4) = 0 Combine like terms: 4m2 + -18m2 = -14m2 (8 + -14m2 + 4m2 + 6m3 + -6m3 + 2m4) = 0 Combine like terms: -14m2 + 4m2 = -10m2 (8 + -10m2 + 6m3 + -6m3 + 2m4) = 0 Combine like terms: 6m3 + -6m3 = 0 (8 + -10m2 + 0 + 2m4) = 0 (8 + -10m2 + 2m4) = 0 Solving 8 + -10m2 + 2m4 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -5m2 + m4) = 0 Factor a trinomial. 2((1 + -1m2)(4 + -1m2)) = 0 Factor a difference between two squares. 2(((1 + m)(1 + -1m))(4 + -1m2)) = 0 Factor a difference between two squares. 2(((2 + m)(2 + -1m))(1 + m)(1 + -1m)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + m)' equal to zero and attempt to solve: Simplifying 1 + m = 0 Solving 1 + m = 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 + m = 0 + -1 Combine like terms: 1 + -1 = 0 0 + m = 0 + -1 m = 0 + -1 Combine like terms: 0 + -1 = -1 m = -1 Simplifying m = -1Subproblem 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 = 1Subproblem 3
Set the factor '(2 + m)' equal to zero and attempt to solve: Simplifying 2 + m = 0 Solving 2 + m = 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 + m = 0 + -2 Combine like terms: 2 + -2 = 0 0 + m = 0 + -2 m = 0 + -2 Combine like terms: 0 + -2 = -2 m = -2 Simplifying m = -2Subproblem 4
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 = 2Solution
m = {-1, 1, -2, 2}
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