2a^2+4a^3+8a^4=

Solution for 2a^2+4a^3+8a^4= equation:

Simplifying
2a2 + 4a3 + 8a4 = 0

Solving
2a2 + 4a3 + 8a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a2'.
2a2(1 + 2a + 4a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}
Subproblem 2
Set the factor '(1 + 2a + 4a2)' equal to zero and attempt to solve:

Simplifying
1 + 2a + 4a2 = 0

Solving
1 + 2a + 4a2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
0.25 + 0.5a + a2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 0.5a + -0.25 + a2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 0.5a + a2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 0.5a + a2 = 0 + -0.25
0.5a + a2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
0.5a + a2 = -0.25

The a term is 0.5a.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5a + 0.0625 + a2 = -0.25 + 0.0625

Reorder the terms:
0.0625 + 0.5a + a2 = -0.25 + 0.0625

Combine like terms: -0.25 + 0.0625 = -0.1875
0.0625 + 0.5a + a2 = -0.1875

Factor a perfect square on the left side:
(a + 0.25)(a + 0.25) = -0.1875

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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