-5n^2+3n+224=0

Solution for -5n^2+3n+224=0 equation:

Simplifying
-5n2 + 3n + 224 = 0

Reorder the terms:
224 + 3n + -5n2 = 0

Solving
224 + 3n + -5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(7 + -1n)(32 + 5n) = 0

Subproblem 1
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Subproblem 2
Set the factor '(32 + 5n)' equal to zero and attempt to solve:

Simplifying
32 + 5n = 0

Solving
32 + 5n = 0

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

Add '-32' to each side of the equation.
32 + -32 + 5n = 0 + -32

Combine like terms: 32 + -32 = 0
0 + 5n = 0 + -32
5n = 0 + -32

Combine like terms: 0 + -32 = -32
5n = -32

Divide each side by '5'.
n = -6.4

Simplifying
n = -6.4
Solution
n = {7, -6.4}