4n^2-5n=-1

Solution for 4n^2-5n=-1 equation:

Simplifying
4n2 + -5n = -1

Reorder the terms:
-5n + 4n2 = -1

Solving
-5n + 4n2 = -1

Solving for variable 'n'.

Reorder the terms:
1 + -5n + 4n2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -5n + 4n2 = 0

Factor a trinomial.
(1 + -4n)(1 + -1n) = 0

Subproblem 1
Set the factor '(1 + -4n)' equal to zero and attempt to solve:

Simplifying
1 + -4n = 0

Solving
1 + -4n = 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 + -4n = 0 + -1

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

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

Divide each side by '-4'.
n = 0.25

Simplifying
n = 0.25
Subproblem 2
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
Solution
n = {0.25, 1}