4n^2+2n-1806=0

Solution for 4n^2+2n-1806=0 equation:

Simplifying
4n2 + 2n + -1806 = 0

Reorder the terms:
-1806 + 2n + 4n2 = 0

Solving
-1806 + 2n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-903 + n + 2n2) = 0

Factor a trinomial.
2((-43 + -2n)(21 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-43 + -2n)' equal to zero and attempt to solve:

Simplifying
-43 + -2n = 0

Solving
-43 + -2n = 0

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

Add '43' to each side of the equation.
-43 + 43 + -2n = 0 + 43

Combine like terms: -43 + 43 = 0
0 + -2n = 0 + 43
-2n = 0 + 43

Combine like terms: 0 + 43 = 43
-2n = 43

Divide each side by '-2'.
n = -21.5

Simplifying
n = -21.5
Subproblem 2
Set the factor '(21 + -1n)' equal to zero and attempt to solve:

Simplifying
21 + -1n = 0

Solving
21 + -1n = 0

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

Add '-21' to each side of the equation.
21 + -21 + -1n = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1n = 0 + -21
-1n = 0 + -21

Combine like terms: 0 + -21 = -21
-1n = -21

Divide each side by '-1'.
n = 21

Simplifying
n = 21
Solution
n = {-21.5, 21}