3m^2+5m=m^2-7m-18

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Solution for 3m^2+5m=m^2-7m-18 equation:


Simplifying
3m2 + 5m = m2 + -7m + -18

Reorder the terms:
5m + 3m2 = m2 + -7m + -18

Reorder the terms:
5m + 3m2 = -18 + -7m + m2

Solving
5m + 3m2 = -18 + -7m + m2

Solving for variable 'm'.

Reorder the terms:
18 + 5m + 7m + 3m2 + -1m2 = -18 + -7m + m2 + 18 + 7m + -1m2

Combine like terms: 5m + 7m = 12m
18 + 12m + 3m2 + -1m2 = -18 + -7m + m2 + 18 + 7m + -1m2

Combine like terms: 3m2 + -1m2 = 2m2
18 + 12m + 2m2 = -18 + -7m + m2 + 18 + 7m + -1m2

Reorder the terms:
18 + 12m + 2m2 = -18 + 18 + -7m + 7m + m2 + -1m2

Combine like terms: -18 + 18 = 0
18 + 12m + 2m2 = 0 + -7m + 7m + m2 + -1m2
18 + 12m + 2m2 = -7m + 7m + m2 + -1m2

Combine like terms: -7m + 7m = 0
18 + 12m + 2m2 = 0 + m2 + -1m2
18 + 12m + 2m2 = m2 + -1m2

Combine like terms: m2 + -1m2 = 0
18 + 12m + 2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 6m + m2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(3 + m)' equal to zero and attempt to solve: Simplifying 3 + m = 0 Solving 3 + m = 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 + m = 0 + -3 Combine like terms: 3 + -3 = 0 0 + m = 0 + -3 m = 0 + -3 Combine like terms: 0 + -3 = -3 m = -3 Simplifying m = -3

Subproblem 2

Set the factor '(3 + m)' equal to zero and attempt to solve: Simplifying 3 + m = 0 Solving 3 + m = 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 + m = 0 + -3 Combine like terms: 3 + -3 = 0 0 + m = 0 + -3 m = 0 + -3 Combine like terms: 0 + -3 = -3 m = -3 Simplifying m = -3

Solution

m = {-3, -3}

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