3n^2-2n-6=10

Solution for 3n^2-2n-6=10 equation:

Simplifying
3n2 + -2n + -6 = 10

Reorder the terms:
-6 + -2n + 3n2 = 10

Solving
-6 + -2n + 3n2 = 10

Solving for variable 'n'.

Reorder the terms:
-6 + -10 + -2n + 3n2 = 10 + -10

Combine like terms: -6 + -10 = -16
-16 + -2n + 3n2 = 10 + -10

Combine like terms: 10 + -10 = 0
-16 + -2n + 3n2 = 0

Factor a trinomial.
(-2 + -1n)(8 + -3n) = 0

Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve:

Simplifying
-2 + -1n = 0

Solving
-2 + -1n = 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 + -1n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1n = 0 + 2
-1n = 0 + 2

Combine like terms: 0 + 2 = 2
-1n = 2

Divide each side by '-1'.
n = -2

Simplifying
n = -2
Subproblem 2
Set the factor '(8 + -3n)' equal to zero and attempt to solve:

Simplifying
8 + -3n = 0

Solving
8 + -3n = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3n = 0 + -8
-3n = 0 + -8

Combine like terms: 0 + -8 = -8
-3n = -8

Divide each side by '-3'.
n = 2.666666667

Simplifying
n = 2.666666667
Solution
n = {-2, 2.666666667}