5n(n-3)=25

Solution for 5n(n-3)=25 equation:

Simplifying
5n(n + -3) = 25

Reorder the terms:
5n(-3 + n) = 25
(-3 * 5n + n * 5n) = 25
(-15n + 5n2) = 25

Solving
-15n + 5n2 = 25

Solving for variable 'n'.

Reorder the terms:
-25 + -15n + 5n2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + -15n + 5n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-5 + -3n + n2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-5 + -3n + n2)' equal to zero and attempt to solve:

Simplifying
-5 + -3n + n2 = 0

Solving
-5 + -3n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -3n + 5 + n2 = 0 + 5

Reorder the terms:
-5 + 5 + -3n + n2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3n + n2 = 0 + 5
-3n + n2 = 0 + 5

Combine like terms: 0 + 5 = 5
-3n + n2 = 5

The n term is -3n.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3n + 2.25 + n2 = 5 + 2.25

Reorder the terms:
2.25 + -3n + n2 = 5 + 2.25

Combine like terms: 5 + 2.25 = 7.25
2.25 + -3n + n2 = 7.25

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(n + -1.5) equal to 2.692582404 and -2.692582404.

Subproblem 1
n + -1.5 = 2.692582404

Simplifying
n + -1.5 = 2.692582404

Reorder the terms:
-1.5 + n = 2.692582404

Solving
-1.5 + n = 2.692582404

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = 2.692582404 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = 2.692582404 + 1.5
n = 2.692582404 + 1.5

Combine like terms: 2.692582404 + 1.5 = 4.192582404
n = 4.192582404

Simplifying
n = 4.192582404

Subproblem 2
n + -1.5 = -2.692582404

Simplifying
n + -1.5 = -2.692582404

Reorder the terms:
-1.5 + n = -2.692582404

Solving
-1.5 + n = -2.692582404

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = -2.692582404 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = -2.692582404 + 1.5
n = -2.692582404 + 1.5

Combine like terms: -2.692582404 + 1.5 = -1.192582404
n = -1.192582404

Simplifying
n = -1.192582404

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {4.192582404, -1.192582404}
Solution
n = {4.192582404, -1.192582404}