n(3n+27)=30

Solution for n(3n+27)=30 equation:

Simplifying
n(3n + 27) = 30

Reorder the terms:
n(27 + 3n) = 30
(27 * n + 3n * n) = 30
(27n + 3n2) = 30

Solving
27n + 3n2 = 30

Solving for variable 'n'.

Reorder the terms:
-30 + 27n + 3n2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 27n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + 9n + n2) = 0

Factor a trinomial.
3((-10 + -1n)(1 + -1n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-10 + -1n)' equal to zero and attempt to solve:

Simplifying
-10 + -1n = 0

Solving
-10 + -1n = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1n = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1n = 0 + 10
-1n = 0 + 10

Combine like terms: 0 + 10 = 10
-1n = 10

Divide each side by '-1'.
n = -10

Simplifying
n = -10
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 = {-10, 1}