6n^2+n+4n^2=

Solution for 6n^2+n+4n^2= equation:

Simplifying
6n2 + n + 4n2 = 0

Reorder the terms:
n + 6n2 + 4n2 = 0

Combine like terms: 6n2 + 4n2 = 10n2
n + 10n2 = 0

Solving
n + 10n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(1 + 10n) = 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 + 10n)' equal to zero and attempt to solve:

Simplifying
1 + 10n = 0

Solving
1 + 10n = 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 + 10n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 10n = 0 + -1
10n = 0 + -1

Combine like terms: 0 + -1 = -1
10n = -1

Divide each side by '10'.
n = -0.1

Simplifying
n = -0.1
Solution
n = {0, -0.1}