105=8m+m^2

Solution for 105=8m+m^2 equation:

Simplifying
105 = 8m + m2

Solving
105 = 8m + m2

Solving for variable 'm'.

Reorder the terms:
105 + -8m + -1m2 = 8m + -8m + m2 + -1m2

Combine like terms: 8m + -8m = 0
105 + -8m + -1m2 = 0 + m2 + -1m2
105 + -8m + -1m2 = m2 + -1m2

Combine like terms: m2 + -1m2 = 0
105 + -8m + -1m2 = 0

Factor a trinomial.
(7 + -1m)(15 + m) = 0

Subproblem 1
Set the factor '(7 + -1m)' equal to zero and attempt to solve:

Simplifying
7 + -1m = 0

Solving
7 + -1m = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1m = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1m = 0 + -7
-1m = 0 + -7

Combine like terms: 0 + -7 = -7
-1m = -7

Divide each side by '-1'.
m = 7

Simplifying
m = 7
Subproblem 2
Set the factor '(15 + m)' equal to zero and attempt to solve:

Simplifying
15 + m = 0

Solving
15 + m = 0

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

Add '-15' to each side of the equation.
15 + -15 + m = 0 + -15

Combine like terms: 15 + -15 = 0
0 + m = 0 + -15
m = 0 + -15

Combine like terms: 0 + -15 = -15
m = -15

Simplifying
m = -15
Solution
m = {7, -15}