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

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


Simplifying
3m2 = m2 + 7m + -5

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

Solving
3m2 = -5 + 7m + m2

Solving for variable 'm'.

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

Combine like terms: 3m2 + -1m2 = 2m2
5 + -7m + 2m2 = -5 + 7m + m2 + 5 + -7m + -1m2

Reorder the terms:
5 + -7m + 2m2 = -5 + 5 + 7m + -7m + m2 + -1m2

Combine like terms: -5 + 5 = 0
5 + -7m + 2m2 = 0 + 7m + -7m + m2 + -1m2
5 + -7m + 2m2 = 7m + -7m + m2 + -1m2

Combine like terms: 7m + -7m = 0
5 + -7m + 2m2 = 0 + m2 + -1m2
5 + -7m + 2m2 = m2 + -1m2

Combine like terms: m2 + -1m2 = 0
5 + -7m + 2m2 = 0

Factor a trinomial.
(1 + -1m)(5 + -2m) = 0


Subproblem 1
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 = 1

Subproblem 2
Set the factor '(5 + -2m)' equal to zero and attempt to solve:

Simplifying
5 + -2m = 0

Solving
5 + -2m = 0

Move all terms containing m to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -2m = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2m = 0 + -5
-2m = 0 + -5

Combine like terms: 0 + -5 = -5
-2m = -5

Divide each side by '-2'.
m = 2.5

Simplifying
m = 2.5
Solution
m = {1, 2.5}

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