4n^2+6n+2n+3-323=0

Solution for 4n^2+6n+2n+3-323=0 equation:

Simplifying
4n2 + 6n + 2n + 3 + -323 = 0

Reorder the terms:
3 + -323 + 6n + 2n + 4n2 = 0

Combine like terms: 3 + -323 = -320
-320 + 6n + 2n + 4n2 = 0

Combine like terms: 6n + 2n = 8n
-320 + 8n + 4n2 = 0

Solving
-320 + 8n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-80 + 2n + n2) = 0

Factor a trinomial.
4((-10 + -1n)(8 + -1n)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-10 + -1n)' equal to zero and attempt to solve:

Simplifying
-10 + -1n = 0

Solving
-10 + -1n = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1n = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1n = 0 + 10
-1n = 0 + 10

Combine like terms: 0 + 10 = 10
-1n = 10

Divide each side by '-1'.
n = -10

Simplifying
n = -10
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 = {-10, 8}