n^2=5n-4

Solution for n^2=5n-4 equation:

Simplifying
n2 = 5n + -4

Reorder the terms:
n2 = -4 + 5n

Solving
n2 = -4 + 5n

Solving for variable 'n'.

Reorder the terms:
4 + -5n + n2 = -4 + 5n + 4 + -5n

Reorder the terms:
4 + -5n + n2 = -4 + 4 + 5n + -5n

Combine like terms: -4 + 4 = 0
4 + -5n + n2 = 0 + 5n + -5n
4 + -5n + n2 = 5n + -5n

Combine like terms: 5n + -5n = 0
4 + -5n + n2 = 0

Factor a trinomial.
(1 + -1n)(4 + -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 '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {1, 4}