4z^2+6z+6=0

Solution for 4z^2+6z+6=0 equation:

Simplifying
4z2 + 6z + 6 = 0

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

Solving
6 + 6z + 4z2 = 0

Solving for variable 'z'.

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

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 3z + 2z2)' equal to zero and attempt to solve:

Simplifying
3 + 3z + 2z2 = 0

Solving
3 + 3z + 2z2 = 0

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

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

Move the constant term to the right:

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

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

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 1.5z + z2 = 0 + -1.5
1.5z + z2 = 0 + -1.5

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

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 = -1.5 + 0.5625

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

Combine like terms: -1.5 + 0.5625 = -0.9375
0.5625 + 1.5z + z2 = -0.9375

Factor a perfect square on the left side:
(z + 0.75)(z + 0.75) = -0.9375

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.

The solution to this equation could not be determined.