6+z+z^2+z=0

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

Simplifying
6 + z + z2 + z = 0

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

Combine like terms: z + z = 2z
6 + 2z + z2 = 0

Solving
6 + 2z + 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 + 2z + -6 + z2 = 0 + -6

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

Combine like terms: 6 + -6 = 0
0 + 2z + z2 = 0 + -6
2z + z2 = 0 + -6

Combine like terms: 0 + -6 = -6
2z + z2 = -6

The z term is 2z.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2z + 1 + z2 = -6 + 1

Reorder the terms:
1 + 2z + z2 = -6 + 1

Combine like terms: -6 + 1 = -5
1 + 2z + z2 = -5

Factor a perfect square on the left side:
(z + 1)(z + 1) = -5

Can't calculate square root of the right side.

The solution to this equation could not be determined.