-5n^2+4n+57=0

Solution for -5n^2+4n+57=0 equation:

Simplifying
-5n2 + 4n + 57 = 0

Reorder the terms:
57 + 4n + -5n2 = 0

Solving
57 + 4n + -5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(19 + -5n)(3 + n) = 0

Subproblem 1
Set the factor '(19 + -5n)' equal to zero and attempt to solve:

Simplifying
19 + -5n = 0

Solving
19 + -5n = 0

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

Add '-19' to each side of the equation.
19 + -19 + -5n = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -5n = 0 + -19
-5n = 0 + -19

Combine like terms: 0 + -19 = -19
-5n = -19

Divide each side by '-5'.
n = 3.8

Simplifying
n = 3.8
Subproblem 2
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

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

Add '-3' to each side of the equation.
3 + -3 + n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + n = 0 + -3
n = 0 + -3

Combine like terms: 0 + -3 = -3
n = -3

Simplifying
n = -3
Solution
n = {3.8, -3}