8a^4-5a^2+4a^3=

Solution for 8a^4-5a^2+4a^3= equation:

Simplifying
8a4 + -5a2 + 4a3 = 0

Reorder the terms:
-5a2 + 4a3 + 8a4 = 0

Solving
-5a2 + 4a3 + 8a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a2'.
a2(-5 + 4a + 8a2) = 0

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 '(-5 + 4a + 8a2)' equal to zero and attempt to solve:

Simplifying
-5 + 4a + 8a2 = 0

Solving
-5 + 4a + 8a2 = 0

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

Divide each side by '8'.
-0.625 + 0.5a + a2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + 0.5a + 0.625 + a2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + 0.5a + a2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + 0.5a + a2 = 0 + 0.625
0.5a + a2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
0.5a + a2 = 0.625

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 = 0.625 + 0.0625

Reorder the terms:
0.0625 + 0.5a + a2 = 0.625 + 0.0625

Combine like terms: 0.625 + 0.0625 = 0.6875
0.0625 + 0.5a + a2 = 0.6875

Factor a perfect square on the left side:
(a + 0.25)(a + 0.25) = 0.6875

Calculate the square root of the right side: 0.829156198

Break this problem into two subproblems by setting 
(a + 0.25) equal to 0.829156198 and -0.829156198.

Subproblem 1
a + 0.25 = 0.829156198

Simplifying
a + 0.25 = 0.829156198

Reorder the terms:
0.25 + a = 0.829156198

Solving
0.25 + a = 0.829156198

Solving for variable 'a'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + a = 0.829156198 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + a = 0.829156198 + -0.25
a = 0.829156198 + -0.25

Combine like terms: 0.829156198 + -0.25 = 0.579156198
a = 0.579156198

Simplifying
a = 0.579156198

Subproblem 2
a + 0.25 = -0.829156198

Simplifying
a + 0.25 = -0.829156198

Reorder the terms:
0.25 + a = -0.829156198

Solving
0.25 + a = -0.829156198

Solving for variable 'a'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + a = -0.829156198 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + a = -0.829156198 + -0.25
a = -0.829156198 + -0.25

Combine like terms: -0.829156198 + -0.25 = -1.079156198
a = -1.079156198

Simplifying
a = -1.079156198

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.579156198, -1.079156198}
Solution
a = {0, 0.579156198, -1.079156198}