n^2+400=40n

Solution for n^2+400=40n equation:

Simplifying
n2 + 400 = 40n

Reorder the terms:
400 + n2 = 40n

Solving
400 + n2 = 40n

Solving for variable 'n'.

Reorder the terms:
400 + -40n + n2 = 40n + -40n

Combine like terms: 40n + -40n = 0
400 + -40n + n2 = 0

Factor a trinomial.
(20 + -1n)(20 + -1n) = 0

Subproblem 1
Set the factor '(20 + -1n)' equal to zero and attempt to solve:

Simplifying
20 + -1n = 0

Solving
20 + -1n = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1n = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1n = 0 + -20
-1n = 0 + -20

Combine like terms: 0 + -20 = -20
-1n = -20

Divide each side by '-1'.
n = 20

Simplifying
n = 20
Subproblem 2
Set the factor '(20 + -1n)' equal to zero and attempt to solve:

Simplifying
20 + -1n = 0

Solving
20 + -1n = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1n = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1n = 0 + -20
-1n = 0 + -20

Combine like terms: 0 + -20 = -20
-1n = -20

Divide each side by '-1'.
n = 20

Simplifying
n = 20
Solution
n = {20, 20}