4z^2+8z+12=0

Solution for 4z^2+8z+12=0 equation:

Simplifying
4z2 + 8z + 12 = 0

Reorder the terms:
12 + 8z + 4z2 = 0

Solving
12 + 8z + 4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 2z + z2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + 2z + z2)' equal to zero and attempt to solve:

Simplifying
3 + 2z + z2 = 0

Solving
3 + 2z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 2z + -3 + z2 = 0 + -3

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

Combine like terms: 3 + -3 = 0
0 + 2z + z2 = 0 + -3
2z + z2 = 0 + -3

Combine like terms: 0 + -3 = -3
2z + z2 = -3

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 = -3 + 1

Reorder the terms:
1 + 2z + z2 = -3 + 1

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

Factor a perfect square on the left side:
(z + 1)(z + 1) = -2

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.