10m^2+3n-8+3m^2-3n+3=0

Solution for 10m^2+3n-8+3m^2-3n+3=0 equation:

Simplifying
10m2 + 3n + -8 + 3m2 + -3n + 3 = 0

Reorder the terms:
-8 + 3 + 10m2 + 3m2 + 3n + -3n = 0

Combine like terms: -8 + 3 = -5
-5 + 10m2 + 3m2 + 3n + -3n = 0

Combine like terms: 10m2 + 3m2 = 13m2
-5 + 13m2 + 3n + -3n = 0

Combine like terms: 3n + -3n = 0
-5 + 13m2 + 0 = 0
-5 + 13m2 = 0

Solving
-5 + 13m2 = 0

Solving for variable 'm'.

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

Add '5' to each side of the equation.
-5 + 5 + 13m2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 13m2 = 0 + 5
13m2 = 0 + 5

Combine like terms: 0 + 5 = 5
13m2 = 5

Divide each side by '13'.
m2 = 0.3846153846

Simplifying
m2 = 0.3846153846

Take the square root of each side:
m = {-0.620173673, 0.620173673}