(m+6)+m+(m*m)=86

Solution for (m+6)+m+(m*m)=86 equation:

Simplifying
(m + 6) + m + (m * m) = 86

Reorder the terms:
(6 + m) + m + (m * m) = 86

Remove parenthesis around (6 + m)
6 + m + m + (m * m) = 86

Multiply m * m
6 + m + m + (m2) = 86
6 + m + m + m2 = 86

Combine like terms: m + m = 2m
6 + 2m + m2 = 86

Solving
6 + 2m + m2 = 86

Solving for variable 'm'.

Reorder the terms:
6 + -86 + 2m + m2 = 86 + -86

Combine like terms: 6 + -86 = -80
-80 + 2m + m2 = 86 + -86

Combine like terms: 86 + -86 = 0
-80 + 2m + m2 = 0

Factor a trinomial.
(-10 + -1m)(8 + -1m) = 0

Subproblem 1
Set the factor '(-10 + -1m)' equal to zero and attempt to solve:

Simplifying
-10 + -1m = 0

Solving
-10 + -1m = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1m = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1m = 0 + 10
-1m = 0 + 10

Combine like terms: 0 + 10 = 10
-1m = 10

Divide each side by '-1'.
m = -10

Simplifying
m = -10
Subproblem 2
Set the factor '(8 + -1m)' equal to zero and attempt to solve:

Simplifying
8 + -1m = 0

Solving
8 + -1m = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1m = 0 + -8

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

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

Divide each side by '-1'.
m = 8

Simplifying
m = 8
Solution
m = {-10, 8}