8m^2+86m+117=9+2m

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Solution for 8m^2+86m+117=9+2m equation:


Simplifying
8m2 + 86m + 117 = 9 + 2m

Reorder the terms:
117 + 86m + 8m2 = 9 + 2m

Solving
117 + 86m + 8m2 = 9 + 2m

Solving for variable 'm'.

Reorder the terms:
117 + -9 + 86m + -2m + 8m2 = 9 + 2m + -9 + -2m

Combine like terms: 117 + -9 = 108
108 + 86m + -2m + 8m2 = 9 + 2m + -9 + -2m

Combine like terms: 86m + -2m = 84m
108 + 84m + 8m2 = 9 + 2m + -9 + -2m

Reorder the terms:
108 + 84m + 8m2 = 9 + -9 + 2m + -2m

Combine like terms: 9 + -9 = 0
108 + 84m + 8m2 = 0 + 2m + -2m
108 + 84m + 8m2 = 2m + -2m

Combine like terms: 2m + -2m = 0
108 + 84m + 8m2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(27 + 21m + 2m2) = 0

Factor a trinomial.
4((9 + m)(3 + 2m)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(9 + m)' equal to zero and attempt to solve: Simplifying 9 + m = 0 Solving 9 + m = 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 + m = 0 + -9 Combine like terms: 9 + -9 = 0 0 + m = 0 + -9 m = 0 + -9 Combine like terms: 0 + -9 = -9 m = -9 Simplifying m = -9

Subproblem 2

Set the factor '(3 + 2m)' equal to zero and attempt to solve: Simplifying 3 + 2m = 0 Solving 3 + 2m = 0 Move all terms containing m to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2m = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2m = 0 + -3 2m = 0 + -3 Combine like terms: 0 + -3 = -3 2m = -3 Divide each side by '2'. m = -1.5 Simplifying m = -1.5

Solution

m = {-9, -1.5}

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