30=3n(n-3)

Solution for 30=3n(n-3) equation:

Simplifying
30 = 3n(n + -3)

Reorder the terms:
30 = 3n(-3 + n)
30 = (-3 * 3n + n * 3n)
30 = (-9n + 3n2)

Solving
30 = -9n + 3n2

Solving for variable 'n'.

Reorder the terms:
30 + 9n + -3n2 = -9n + 9n + 3n2 + -3n2

Combine like terms: -9n + 9n = 0
30 + 9n + -3n2 = 0 + 3n2 + -3n2
30 + 9n + -3n2 = 3n2 + -3n2

Combine like terms: 3n2 + -3n2 = 0
30 + 9n + -3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + 3n + -1n2) = 0

Factor a trinomial.
3((5 + -1n)(2 + n)) = 0

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

Simplifying
5 + -1n = 0

Solving
5 + -1n = 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 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

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

Simplifying
2 + n = 0

Solving
2 + n = 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 + n = 0 + -2

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

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

Simplifying
n = -2
Solution
n = {5, -2}