m^2-20m+61=10

Solution for m^2-20m+61=10 equation:

Simplifying
m2 + -20m + 61 = 10

Reorder the terms:
61 + -20m + m2 = 10

Solving
61 + -20m + m2 = 10

Solving for variable 'm'.

Reorder the terms:
61 + -10 + -20m + m2 = 10 + -10

Combine like terms: 61 + -10 = 51
51 + -20m + m2 = 10 + -10

Combine like terms: 10 + -10 = 0
51 + -20m + m2 = 0

Factor a trinomial.
(3 + -1m)(17 + -1m) = 0

Subproblem 1
Set the factor '(3 + -1m)' equal to zero and attempt to solve:

Simplifying
3 + -1m = 0

Solving
3 + -1m = 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 + -1m = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1m = 0 + -3
-1m = 0 + -3

Combine like terms: 0 + -3 = -3
-1m = -3

Divide each side by '-1'.
m = 3

Simplifying
m = 3
Subproblem 2
Set the factor '(17 + -1m)' equal to zero and attempt to solve:

Simplifying
17 + -1m = 0

Solving
17 + -1m = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1m = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1m = 0 + -17
-1m = 0 + -17

Combine like terms: 0 + -17 = -17
-1m = -17

Divide each side by '-1'.
m = 17

Simplifying
m = 17
Solution
m = {3, 17}