2z^2+4z+8=0

Solution for 2z^2+4z+8=0 equation:

Simplifying
2z2 + 4z + 8 = 0

Reorder the terms:
8 + 4z + 2z2 = 0

Solving
8 + 4z + 2z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 2z + z2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + 2z + z2)' equal to zero and attempt to solve:

Simplifying
4 + 2z + z2 = 0

Solving
4 + 2z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 2z + -4 + z2 = 0 + -4

Reorder the terms:
4 + -4 + 2z + z2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 2z + z2 = 0 + -4
2z + z2 = 0 + -4

Combine like terms: 0 + -4 = -4
2z + z2 = -4

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 = -4 + 1

Reorder the terms:
1 + 2z + z2 = -4 + 1

Combine like terms: -4 + 1 = -3
1 + 2z + z2 = -3

Factor a perfect square on the left side:
(z + 1)(z + 1) = -3

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.