6z^2+2z+3=

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

Simplifying
6z2 + 2z + 3 = 0

Reorder the terms:
3 + 2z + 6z2 = 0

Solving
3 + 2z + 6z2 = 0

Solving for variable 'z'.

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

Divide each side by '6'.
0.5 + 0.3333333333z + z2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 0.3333333333z + -0.5 + z2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 0.3333333333z + z2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 0.3333333333z + z2 = 0 + -0.5
0.3333333333z + z2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
0.3333333333z + z2 = -0.5

The z term is 0.3333333333z.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333z + 0.02777777779 + z2 = -0.5 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333z + z2 = -0.5 + 0.02777777779

Combine like terms: -0.5 + 0.02777777779 = -0.47222222221
0.02777777779 + 0.3333333333z + z2 = -0.47222222221

Factor a perfect square on the left side:
(z + 0.1666666667)(z + 0.1666666667) = -0.47222222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.