n^2+4n^2-9n+6-8=0

Solution for n^2+4n^2-9n+6-8=0 equation:

Simplifying
n2 + 4n2 + -9n + 6 + -8 = 0

Reorder the terms:
6 + -8 + -9n + n2 + 4n2 = 0

Combine like terms: 6 + -8 = -2
-2 + -9n + n2 + 4n2 = 0

Combine like terms: n2 + 4n2 = 5n2
-2 + -9n + 5n2 = 0

Solving
-2 + -9n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -5n)(2 + -1n) = 0

Subproblem 1
Set the factor '(-1 + -5n)' equal to zero and attempt to solve:

Simplifying
-1 + -5n = 0

Solving
-1 + -5n = 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 + -5n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5n = 0 + 1
-5n = 0 + 1

Combine like terms: 0 + 1 = 1
-5n = 1

Divide each side by '-5'.
n = -0.2

Simplifying
n = -0.2
Subproblem 2
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
Solution
n = {-0.2, 2}