2m^2=15-7m

Solution for 2m^2=15-7m equation:

Simplifying
2m2 = 15 + -7m

Solving
2m2 = 15 + -7m

Solving for variable 'm'.

Reorder the terms:
-15 + 7m + 2m2 = 15 + -7m + -15 + 7m

Reorder the terms:
-15 + 7m + 2m2 = 15 + -15 + -7m + 7m

Combine like terms: 15 + -15 = 0
-15 + 7m + 2m2 = 0 + -7m + 7m
-15 + 7m + 2m2 = -7m + 7m

Combine like terms: -7m + 7m = 0
-15 + 7m + 2m2 = 0

Factor a trinomial.
(-5 + -1m)(3 + -2m) = 0

Subproblem 1
Set the factor '(-5 + -1m)' equal to zero and attempt to solve:

Simplifying
-5 + -1m = 0

Solving
-5 + -1m = 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 + -1m = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1m = 0 + 5
-1m = 0 + 5

Combine like terms: 0 + 5 = 5
-1m = 5

Divide each side by '-1'.
m = -5

Simplifying
m = -5
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 = {-5, 1.5}