f(a)=2a^3+4a

Solution for f(a)=2a^3+4a equation:

Simplifying
f(a) = 2a3 + 4a

Multiply f * a
af = 2a3 + 4a

Reorder the terms:
af = 4a + 2a3

Solving
af = 4a + 2a3

Solving for variable 'a'.

Reorder the terms:
-4a + af + -2a3 = 4a + 2a3 + -4a + -2a3

Reorder the terms:
-4a + af + -2a3 = 4a + -4a + 2a3 + -2a3

Combine like terms: 4a + -4a = 0
-4a + af + -2a3 = 0 + 2a3 + -2a3
-4a + af + -2a3 = 2a3 + -2a3

Combine like terms: 2a3 + -2a3 = 0
-4a + af + -2a3 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(-4 + f + -2a2) = 0

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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(-4 + f + -2a2)' equal to zero and attempt to solve:

Simplifying
-4 + f + -2a2 = 0

Reorder the terms:
-4 + -2a2 + f = 0

Solving
-4 + -2a2 + f = 0

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

Add '4' to each side of the equation.
-4 + -2a2 + 4 + f = 0 + 4

Reorder the terms:
-4 + 4 + -2a2 + f = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -2a2 + f = 0 + 4
-2a2 + f = 0 + 4

Combine like terms: 0 + 4 = 4
-2a2 + f = 4

Add '-1f' to each side of the equation.
-2a2 + f + -1f = 4 + -1f

Combine like terms: f + -1f = 0
-2a2 + 0 = 4 + -1f
-2a2 = 4 + -1f

Divide each side by '-2'.
a2 = -2 + 0.5f

Simplifying
a2 = -2 + 0.5f

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}