5n^2+75n=3500

Solution for 5n^2+75n=3500 equation:

Simplifying
5n2 + 75n = 3500

Reorder the terms:
75n + 5n2 = 3500

Solving
75n + 5n2 = 3500

Solving for variable 'n'.

Reorder the terms:
-3500 + 75n + 5n2 = 3500 + -3500

Combine like terms: 3500 + -3500 = 0
-3500 + 75n + 5n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-700 + 15n + n2) = 0

Factor a trinomial.
5((-35 + -1n)(20 + -1n)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-35 + -1n)' equal to zero and attempt to solve:

Simplifying
-35 + -1n = 0

Solving
-35 + -1n = 0

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

Add '35' to each side of the equation.
-35 + 35 + -1n = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -1n = 0 + 35
-1n = 0 + 35

Combine like terms: 0 + 35 = 35
-1n = 35

Divide each side by '-1'.
n = -35

Simplifying
n = -35
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 = {-35, 20}