8z^2(5z^2-4z+1)=

Solution for 8z^2(5z^2-4z+1)= equation:

Simplifying
8z2(5z2 + -4z + 1) = 0

Reorder the terms:
8z2(1 + -4z + 5z2) = 0
(1 * 8z2 + -4z * 8z2 + 5z2 * 8z2) = 0
(8z2 + -32z3 + 40z4) = 0

Solving
8z2 + -32z3 + 40z4 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '8z2'.
8z2(1 + -4z + 5z2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve:

Simplifying
z2 = 0

Solving
z2 = 0

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

Simplifying
z2 = 0

Take the square root of each side:
z = {0}
Subproblem 2
Set the factor '(1 + -4z + 5z2)' equal to zero and attempt to solve:

Simplifying
1 + -4z + 5z2 = 0

Solving
1 + -4z + 5z2 = 0

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

Divide each side by '5'.
0.2 + -0.8z + z2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -0.8z + -0.2 + z2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -0.8z + z2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -0.8z + z2 = 0 + -0.2
-0.8z + z2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-0.8z + z2 = -0.2

The z term is -0.8z.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8z + 0.16 + z2 = -0.2 + 0.16

Reorder the terms:
0.16 + -0.8z + z2 = -0.2 + 0.16

Combine like terms: -0.2 + 0.16 = -0.04
0.16 + -0.8z + z2 = -0.04

Factor a perfect square on the left side:
(z + -0.4)(z + -0.4) = -0.04

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
z = {0}