-8z(2z+3z^2+3z^3)=

Solution for -8z(2z+3z^2+3z^3)= equation:

Simplifying
-8z(2z + 3z2 + 3z3) = 0
(2z * -8z + 3z2 * -8z + 3z3 * -8z) = 0
(-16z2 + -24z3 + -24z4) = 0

Solving
-16z2 + -24z3 + -24z4 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '-8z2'.
-8z2(2 + 3z + 3z2) = 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 '(2 + 3z + 3z2)' equal to zero and attempt to solve:

Simplifying
2 + 3z + 3z2 = 0

Solving
2 + 3z + 3z2 = 0

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

Divide each side by '3'.
0.6666666667 + z + z2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + z + -0.6666666667 + z2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + z + z2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + z + z2 = 0 + -0.6666666667
z + z2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
z + z2 = -0.6666666667

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

Add '0.25' to each side of the equation.
 + 0.25 + z2 = -0.6666666667 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + z2 = -0.6666666667 + 0.25

Combine like terms: -0.6666666667 + 0.25 = -0.4166666667
1.25 + z2 = -0.4166666667

Factor a perfect square on the left side:
(z + 0.5)(z + 0.5) = -0.4166666667

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}