5n^2=-25n

Solution for 5n^2=-25n equation:

Simplifying
5n2 = -25n

Solving
5n2 = -25n

Solving for variable 'n'.

Reorder the terms:
25n + 5n2 = -25n + 25n

Combine like terms: -25n + 25n = 0
25n + 5n2 = 0

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

Ignore the factor 5.
Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(5 + n)' equal to zero and attempt to solve:

Simplifying
5 + n = 0

Solving
5 + n = 0

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

Add '-5' to each side of the equation.
5 + -5 + n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + n = 0 + -5
n = 0 + -5

Combine like terms: 0 + -5 = -5
n = -5

Simplifying
n = -5
Solution
n = {0, -5}