n(n-3)=5400

Solution for n(n-3)=5400 equation:

Simplifying
n(n + -3) = 5400

Reorder the terms:
n(-3 + n) = 5400
(-3 * n + n * n) = 5400
(-3n + n2) = 5400

Solving
-3n + n2 = 5400

Solving for variable 'n'.

Reorder the terms:
-5400 + -3n + n2 = 5400 + -5400

Combine like terms: 5400 + -5400 = 0
-5400 + -3n + n2 = 0

Factor a trinomial.
(-72 + -1n)(75 + -1n) = 0

Subproblem 1
Set the factor '(-72 + -1n)' equal to zero and attempt to solve:

Simplifying
-72 + -1n = 0

Solving
-72 + -1n = 0

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

Add '72' to each side of the equation.
-72 + 72 + -1n = 0 + 72

Combine like terms: -72 + 72 = 0
0 + -1n = 0 + 72
-1n = 0 + 72

Combine like terms: 0 + 72 = 72
-1n = 72

Divide each side by '-1'.
n = -72

Simplifying
n = -72
Subproblem 2
Set the factor '(75 + -1n)' equal to zero and attempt to solve:

Simplifying
75 + -1n = 0

Solving
75 + -1n = 0

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

Add '-75' to each side of the equation.
75 + -75 + -1n = 0 + -75

Combine like terms: 75 + -75 = 0
0 + -1n = 0 + -75
-1n = 0 + -75

Combine like terms: 0 + -75 = -75
-1n = -75

Divide each side by '-1'.
n = 75

Simplifying
n = 75
Solution
n = {-72, 75}