n^2-21=20n

Solution for n^2-21=20n equation:

Simplifying
n2 + -21 = 20n

Reorder the terms:
-21 + n2 = 20n

Solving
-21 + n2 = 20n

Solving for variable 'n'.

Reorder the terms:
-21 + -20n + n2 = 20n + -20n

Combine like terms: 20n + -20n = 0
-21 + -20n + n2 = 0

Factor a trinomial.
(-1 + -1n)(21 + -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 '(21 + -1n)' equal to zero and attempt to solve:

Simplifying
21 + -1n = 0

Solving
21 + -1n = 0

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

Add '-21' to each side of the equation.
21 + -21 + -1n = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1n = 0 + -21
-1n = 0 + -21

Combine like terms: 0 + -21 = -21
-1n = -21

Divide each side by '-1'.
n = 21

Simplifying
n = 21
Solution
n = {-1, 21}