6n^2+3n-6=-2n

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

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

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

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

Solving for variable 'n'.

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

Combine like terms: 3n + 2n = 5n
-6 + 5n + 6n2 = -2n + 2n

Combine like terms: -2n + 2n = 0
-6 + 5n + 6n2 = 0

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

Subproblem 1
Set the factor '(-3 + -2n)' equal to zero and attempt to solve:

Simplifying
-3 + -2n = 0

Solving
-3 + -2n = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2n = 0 + 3
-2n = 0 + 3

Combine like terms: 0 + 3 = 3
-2n = 3

Divide each side by '-2'.
n = -1.5

Simplifying
n = -1.5
Subproblem 2
Set the factor '(2 + -3n)' equal to zero and attempt to solve:

Simplifying
2 + -3n = 0

Solving
2 + -3n = 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 + -3n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3n = 0 + -2
-3n = 0 + -2

Combine like terms: 0 + -2 = -2
-3n = -2

Divide each side by '-3'.
n = 0.6666666667

Simplifying
n = 0.6666666667
Solution
n = {-1.5, 0.6666666667}