4z^3+6z^2+12z=

Solution for 4z^3+6z^2+12z= equation:

Simplifying
4z3 + 6z2 + 12z = 0

Reorder the terms:
12z + 6z2 + 4z3 = 0

Solving
12z + 6z2 + 4z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2z'.
2z(6 + 3z + 2z2) = 0

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

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
Subproblem 2
Set the factor '(6 + 3z + 2z2)' equal to zero and attempt to solve:

Simplifying
6 + 3z + 2z2 = 0

Solving
6 + 3z + 2z2 = 0

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

Divide each side by '2'.
3 + 1.5z + z2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 1.5z + -3 + z2 = 0 + -3

Reorder the terms:
3 + -3 + 1.5z + z2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 1.5z + z2 = 0 + -3
1.5z + z2 = 0 + -3

Combine like terms: 0 + -3 = -3
1.5z + z2 = -3

The z term is 1.5z.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5z + 0.5625 + z2 = -3 + 0.5625

Reorder the terms:
0.5625 + 1.5z + z2 = -3 + 0.5625

Combine like terms: -3 + 0.5625 = -2.4375
0.5625 + 1.5z + z2 = -2.4375

Factor a perfect square on the left side:
(z + 0.75)(z + 0.75) = -2.4375

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}