250n+50n^2=25000

Solution for 250n+50n^2=25000 equation:

Simplifying
250n + 50n2 = 25000

Solving
250n + 50n2 = 25000

Solving for variable 'n'.

Reorder the terms:
-25000 + 250n + 50n2 = 25000 + -25000

Combine like terms: 25000 + -25000 = 0
-25000 + 250n + 50n2 = 0

Factor out the Greatest Common Factor (GCF), '50'.
50(-500 + 5n + n2) = 0

Factor a trinomial.
50((-25 + -1n)(20 + -1n)) = 0

Ignore the factor 50.
Subproblem 1
Set the factor '(-25 + -1n)' equal to zero and attempt to solve:

Simplifying
-25 + -1n = 0

Solving
-25 + -1n = 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 + -1n = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -1n = 0 + 25
-1n = 0 + 25

Combine like terms: 0 + 25 = 25
-1n = 25

Divide each side by '-1'.
n = -25

Simplifying
n = -25
Subproblem 2
Set the factor '(20 + -1n)' equal to zero and attempt to solve:

Simplifying
20 + -1n = 0

Solving
20 + -1n = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1n = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1n = 0 + -20
-1n = 0 + -20

Combine like terms: 0 + -20 = -20
-1n = -20

Divide each side by '-1'.
n = 20

Simplifying
n = 20
Solution
n = {-25, 20}