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}