f(0)=4n^2+2n

Solution for f(0)=4n^2+2n equation:

Simplifying
f(0) = 4n2 + 2n

Reorder the terms for easier multiplication:
0f = 4n2 + 2n

Anything times zero is zero.
0f = 4n2 + 2n

Reorder the terms:
0 = 2n + 4n2

Solving
0 = 2n + 4n2

Solving for variable 'n'.
Remove the zero:
-2n + -4n2 = 2n + 4n2 + -2n + -4n2

Reorder the terms:
-2n + -4n2 = 2n + -2n + 4n2 + -4n2

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

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

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

Ignore the factor -2.
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}