3m^2-6m+13=10

Solution for 3m^2-6m+13=10 equation:

Simplifying
3m2 + -6m + 13 = 10

Reorder the terms:
13 + -6m + 3m2 = 10

Solving
13 + -6m + 3m2 = 10

Solving for variable 'm'.

Reorder the terms:
13 + -10 + -6m + 3m2 = 10 + -10

Combine like terms: 13 + -10 = 3
3 + -6m + 3m2 = 10 + -10

Combine like terms: 10 + -10 = 0
3 + -6m + 3m2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -2m + m2) = 0

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

Ignore the factor 3.
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 '(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
Solution
m = {1, 1}