m^2+3m=10m-6

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

Simplifying
m2 + 3m = 10m + -6

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

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

Solving
3m + m2 = -6 + 10m

Solving for variable 'm'.

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

Combine like terms: 3m + -10m = -7m
6 + -7m + m2 = -6 + 10m + 6 + -10m

Reorder the terms:
6 + -7m + m2 = -6 + 6 + 10m + -10m

Combine like terms: -6 + 6 = 0
6 + -7m + m2 = 0 + 10m + -10m
6 + -7m + m2 = 10m + -10m

Combine like terms: 10m + -10m = 0
6 + -7m + m2 = 0

Factor a trinomial.
(1 + -1m)(6 + -1m) = 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 '(6 + -1m)' equal to zero and attempt to solve:

Simplifying
6 + -1m = 0

Solving
6 + -1m = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1m = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1m = 0 + -6
-1m = 0 + -6

Combine like terms: 0 + -6 = -6
-1m = -6

Divide each side by '-1'.
m = 6

Simplifying
m = 6
Solution
m = {1, 6}