3n^2-6n=105

Solution for 3n^2-6n=105 equation:

Simplifying
3n2 + -6n = 105

Reorder the terms:
-6n + 3n2 = 105

Solving
-6n + 3n2 = 105

Solving for variable 'n'.

Reorder the terms:
-105 + -6n + 3n2 = 105 + -105

Combine like terms: 105 + -105 = 0
-105 + -6n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-35 + -2n + n2) = 0

Factor a trinomial.
3((-5 + -1n)(7 + -1n)) = 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 '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {-5, 7}