25n(n+1)=50

Solution for 25n(n+1)=50 equation:

Simplifying
25n(n + 1) = 50

Reorder the terms:
25n(1 + n) = 50
(1 * 25n + n * 25n) = 50
(25n + 25n2) = 50

Solving
25n + 25n2 = 50

Solving for variable 'n'.

Reorder the terms:
-50 + 25n + 25n2 = 50 + -50

Combine like terms: 50 + -50 = 0
-50 + 25n + 25n2 = 0

Factor out the Greatest Common Factor (GCF), '25'.
25(-2 + n + n2) = 0

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

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

Simplifying
-2 + -1n = 0

Solving
-2 + -1n = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1n = 0 + 2
-1n = 0 + 2

Combine like terms: 0 + 2 = 2
-1n = 2

Divide each side by '-1'.
n = -2

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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

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

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

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

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

Simplifying
n = 1
Solution
n = {-2, 1}