n^2=10+9n

Solution for n^2=10+9n equation:

Simplifying
n2 = 10 + 9n

Solving
n2 = 10 + 9n

Solving for variable 'n'.

Reorder the terms:
-10 + -9n + n2 = 10 + 9n + -10 + -9n

Reorder the terms:
-10 + -9n + n2 = 10 + -10 + 9n + -9n

Combine like terms: 10 + -10 = 0
-10 + -9n + n2 = 0 + 9n + -9n
-10 + -9n + n2 = 9n + -9n

Combine like terms: 9n + -9n = 0
-10 + -9n + n2 = 0

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

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

Simplifying
-1 + -1n = 0

Solving
-1 + -1n = 0

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

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

Combine like terms: -1 + 1 = 0
0 + -1n = 0 + 1
-1n = 0 + 1

Combine like terms: 0 + 1 = 1
-1n = 1

Divide each side by '-1'.
n = -1

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

Simplifying
10 + -1n = 0

Solving
10 + -1n = 0

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

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

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

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

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

Simplifying
n = 10
Solution
n = {-1, 10}