z^2+3*z+6=0

Solution for z^2+3*z+6=0 equation:

Simplifying
z2 + 3z + 6 = 0

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

Solving
6 + 3z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 3z + -6 + z2 = 0 + -6

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

Combine like terms: 6 + -6 = 0
0 + 3z + z2 = 0 + -6
3z + z2 = 0 + -6

Combine like terms: 0 + -6 = -6
3z + z2 = -6

The z term is 3z.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3z + 2.25 + z2 = -6 + 2.25

Reorder the terms:
2.25 + 3z + z2 = -6 + 2.25

Combine like terms: -6 + 2.25 = -3.75
2.25 + 3z + z2 = -3.75

Factor a perfect square on the left side:
(z + 1.5)(z + 1.5) = -3.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.