4n^2-14n-800=0

Solution for 4n^2-14n-800=0 equation:

Simplifying
4n2 + -14n + -800 = 0

Reorder the terms:
-800 + -14n + 4n2 = 0

Solving
-800 + -14n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-400 + -7n + 2n2) = 0

Factor a trinomial.
2((-25 + -2n)(16 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-25 + -2n)' equal to zero and attempt to solve:

Simplifying
-25 + -2n = 0

Solving
-25 + -2n = 0

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

Add '25' to each side of the equation.
-25 + 25 + -2n = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -2n = 0 + 25
-2n = 0 + 25

Combine like terms: 0 + 25 = 25
-2n = 25

Divide each side by '-2'.
n = -12.5

Simplifying
n = -12.5
Subproblem 2
Set the factor '(16 + -1n)' equal to zero and attempt to solve:

Simplifying
16 + -1n = 0

Solving
16 + -1n = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1n = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1n = 0 + -16
-1n = 0 + -16

Combine like terms: 0 + -16 = -16
-1n = -16

Divide each side by '-1'.
n = 16

Simplifying
n = 16
Solution
n = {-12.5, 16}