8n^2+n-2(n+3n^2)=

Solution for 8n^2+n-2(n+3n^2)= equation:

Simplifying
8n2 + n + -2(n + 3n2) = 0
8n2 + n + (n * -2 + 3n2 * -2) = 0
8n2 + n + (-2n + -6n2) = 0

Reorder the terms:
n + -2n + 8n2 + -6n2 = 0

Combine like terms: n + -2n = -1n
-1n + 8n2 + -6n2 = 0

Combine like terms: 8n2 + -6n2 = 2n2
-1n + 2n2 = 0

Solving
-1n + 2n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(-1 + 2n) = 0

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(-1 + 2n)' equal to zero and attempt to solve:

Simplifying
-1 + 2n = 0

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

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

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

Divide each side by '2'.
n = 0.5

Simplifying
n = 0.5
Solution
n = {0, 0.5}