n-6*3n+1=3n*n-5

Solution for n-6*3n+1=3n*n-5 equation:

Simplifying
n + -6 * 3n + 1 = 3n * n + -5

Multiply -6 * 3
n + -18n + 1 = 3n * n + -5

Reorder the terms:
1 + n + -18n = 3n * n + -5

Combine like terms: n + -18n = -17n
1 + -17n = 3n * n + -5

Multiply n * n
1 + -17n = 3n2 + -5

Reorder the terms:
1 + -17n = -5 + 3n2

Solving
1 + -17n = -5 + 3n2

Solving for variable 'n'.

Reorder the terms:
1 + 5 + -17n + -3n2 = -5 + 3n2 + 5 + -3n2

Combine like terms: 1 + 5 = 6
6 + -17n + -3n2 = -5 + 3n2 + 5 + -3n2

Reorder the terms:
6 + -17n + -3n2 = -5 + 5 + 3n2 + -3n2

Combine like terms: -5 + 5 = 0
6 + -17n + -3n2 = 0 + 3n2 + -3n2
6 + -17n + -3n2 = 3n2 + -3n2

Combine like terms: 3n2 + -3n2 = 0
6 + -17n + -3n2 = 0

Factor a trinomial.
(1 + -3n)(6 + n) = 0

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

Simplifying
1 + -3n = 0

Solving
1 + -3n = 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 + -3n = 0 + -1

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

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

Divide each side by '-3'.
n = 0.3333333333

Simplifying
n = 0.3333333333
Subproblem 2
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 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 + n = 0 + -6

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

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

Simplifying
n = -6
Solution
n = {0.3333333333, -6}