n(n-3)=54

Solution for n(n-3)=54 equation:

Simplifying
n(n + -3) = 54

Reorder the terms:
n(-3 + n) = 54
(-3 * n + n * n) = 54
(-3n + n2) = 54

Solving
-3n + n2 = 54

Solving for variable 'n'.

Reorder the terms:
-54 + -3n + n2 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + -3n + n2 = 0

Factor a trinomial.
(-6 + -1n)(9 + -1n) = 0

Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve:

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1n = 0 + 6
-1n = 0 + 6

Combine like terms: 0 + 6 = 6
-1n = 6

Divide each side by '-1'.
n = -6

Simplifying
n = -6
Subproblem 2
Set the factor '(9 + -1n)' equal to zero and attempt to solve:

Simplifying
9 + -1n = 0

Solving
9 + -1n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1n = 0 + -9
-1n = 0 + -9

Combine like terms: 0 + -9 = -9
-1n = -9

Divide each side by '-1'.
n = 9

Simplifying
n = 9
Solution
n = {-6, 9}