n(3n-1)=234

Solution for n(3n-1)=234 equation:

Simplifying
n(3n + -1) = 234

Reorder the terms:
n(-1 + 3n) = 234
(-1 * n + 3n * n) = 234
(-1n + 3n2) = 234

Solving
-1n + 3n2 = 234

Solving for variable 'n'.

Reorder the terms:
-234 + -1n + 3n2 = 234 + -234

Combine like terms: 234 + -234 = 0
-234 + -1n + 3n2 = 0

Factor a trinomial.
(-26 + -3n)(9 + -1n) = 0

Subproblem 1
Set the factor '(-26 + -3n)' equal to zero and attempt to solve:

Simplifying
-26 + -3n = 0

Solving
-26 + -3n = 0

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

Add '26' to each side of the equation.
-26 + 26 + -3n = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -3n = 0 + 26
-3n = 0 + 26

Combine like terms: 0 + 26 = 26
-3n = 26

Divide each side by '-3'.
n = -8.666666667

Simplifying
n = -8.666666667
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 = {-8.666666667, 9}