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Simplifying 0 = 5m(3m3 + -4m)(7m3 + -2m2 + 5m + 1) Reorder the terms: 0 = 5m(-4m + 3m3)(7m3 + -2m2 + 5m + 1) Reorder the terms: 0 = 5m(-4m + 3m3)(1 + 5m + -2m2 + 7m3) Multiply (-4m + 3m3) * (1 + 5m + -2m2 + 7m3) 0 = 5m(-4m * (1 + 5m + -2m2 + 7m3) + 3m3 * (1 + 5m + -2m2 + 7m3)) 0 = 5m((1 * -4m + 5m * -4m + -2m2 * -4m + 7m3 * -4m) + 3m3 * (1 + 5m + -2m2 + 7m3)) 0 = 5m((-4m + -20m2 + 8m3 + -28m4) + 3m3 * (1 + 5m + -2m2 + 7m3)) 0 = 5m(-4m + -20m2 + 8m3 + -28m4 + (1 * 3m3 + 5m * 3m3 + -2m2 * 3m3 + 7m3 * 3m3)) 0 = 5m(-4m + -20m2 + 8m3 + -28m4 + (3m3 + 15m4 + -6m5 + 21m6)) Reorder the terms: 0 = 5m(-4m + -20m2 + 8m3 + 3m3 + -28m4 + 15m4 + -6m5 + 21m6) Combine like terms: 8m3 + 3m3 = 11m3 0 = 5m(-4m + -20m2 + 11m3 + -28m4 + 15m4 + -6m5 + 21m6) Combine like terms: -28m4 + 15m4 = -13m4 0 = 5m(-4m + -20m2 + 11m3 + -13m4 + -6m5 + 21m6) 0 = (-4m * 5m + -20m2 * 5m + 11m3 * 5m + -13m4 * 5m + -6m5 * 5m + 21m6 * 5m) 0 = (-20m2 + -100m3 + 55m4 + -65m5 + -30m6 + 105m7) Solving 0 = -20m2 + -100m3 + 55m4 + -65m5 + -30m6 + 105m7 Solving for variable 'm'. Remove the zero: 20m2 + 100m3 + -55m4 + 65m5 + 30m6 + -105m7 = -20m2 + -100m3 + 55m4 + -65m5 + -30m6 + 105m7 + 20m2 + 100m3 + -55m4 + 65m5 + 30m6 + -105m7 Reorder the terms: 20m2 + 100m3 + -55m4 + 65m5 + 30m6 + -105m7 = -20m2 + 20m2 + -100m3 + 100m3 + 55m4 + -55m4 + -65m5 + 65m5 + -30m6 + 30m6 + 105m7 + -105m7 Combine like terms: -20m2 + 20m2 = 0 20m2 + 100m3 + -55m4 + 65m5 + 30m6 + -105m7 = 0 + -100m3 + 100m3 + 55m4 + -55m4 + -65m5 + 65m5 + -30m6 + 30m6 + 105m7 + -105m7 20m2 + 100m3 + -55m4 + 65m5 + 30m6 + -105m7 = -100m3 + 100m3 + 55m4 + -55m4 + -65m5 + 65m5 + -30m6 + 30m6 + 105m7 + -105m7 Combine like terms: -100m3 + 100m3 = 0 20m2 + 100m3 + -55m4 + 65m5 + 30m6 + -105m7 = 0 + 55m4 + -55m4 + -65m5 + 65m5 + -30m6 + 30m6 + 105m7 + -105m7 20m2 + 100m3 + -55m4 + 65m5 + 30m6 + -105m7 = 55m4 + -55m4 + -65m5 + 65m5 + -30m6 + 30m6 + 105m7 + -105m7 Combine like terms: 55m4 + -55m4 = 0 20m2 + 100m3 + -55m4 + 65m5 + 30m6 + -105m7 = 0 + -65m5 + 65m5 + -30m6 + 30m6 + 105m7 + -105m7 20m2 + 100m3 + -55m4 + 65m5 + 30m6 + -105m7 = -65m5 + 65m5 + -30m6 + 30m6 + 105m7 + -105m7 Combine like terms: -65m5 + 65m5 = 0 20m2 + 100m3 + -55m4 + 65m5 + 30m6 + -105m7 = 0 + -30m6 + 30m6 + 105m7 + -105m7 20m2 + 100m3 + -55m4 + 65m5 + 30m6 + -105m7 = -30m6 + 30m6 + 105m7 + -105m7 Combine like terms: -30m6 + 30m6 = 0 20m2 + 100m3 + -55m4 + 65m5 + 30m6 + -105m7 = 0 + 105m7 + -105m7 20m2 + 100m3 + -55m4 + 65m5 + 30m6 + -105m7 = 105m7 + -105m7 Combine like terms: 105m7 + -105m7 = 0 20m2 + 100m3 + -55m4 + 65m5 + 30m6 + -105m7 = 0 Factor out the Greatest Common Factor (GCF), '5m2'. 5m2(4 + 20m + -11m2 + 13m3 + 6m4 + -21m5) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'm2' equal to zero and attempt to solve: Simplifying m2 = 0 Solving m2 = 0 Move all terms containing m to the left, all other terms to the right. Simplifying m2 = 0 Take the square root of each side: m = {0}Subproblem 2
Set the factor '(4 + 20m + -11m2 + 13m3 + 6m4 + -21m5)' equal to zero and attempt to solve: Simplifying 4 + 20m + -11m2 + 13m3 + 6m4 + -21m5 = 0 Solving 4 + 20m + -11m2 + 13m3 + 6m4 + -21m5 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
m = {0}
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