5n^2-3n-296=0

Solution for 5n^2-3n-296=0 equation:

Simplifying
5n2 + -3n + -296 = 0

Reorder the terms:
-296 + -3n + 5n2 = 0

Solving
-296 + -3n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-37 + -5n)(8 + -1n) = 0

Subproblem 1
Set the factor '(-37 + -5n)' equal to zero and attempt to solve:

Simplifying
-37 + -5n = 0

Solving
-37 + -5n = 0

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

Add '37' to each side of the equation.
-37 + 37 + -5n = 0 + 37

Combine like terms: -37 + 37 = 0
0 + -5n = 0 + 37
-5n = 0 + 37

Combine like terms: 0 + 37 = 37
-5n = 37

Divide each side by '-5'.
n = -7.4

Simplifying
n = -7.4
Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1n = 0

Solving
8 + -1n = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1n = 0 + -8
-1n = 0 + -8

Combine like terms: 0 + -8 = -8
-1n = -8

Divide each side by '-1'.
n = 8

Simplifying
n = 8
Solution
n = {-7.4, 8}