3z^2+6=-4z

Solution for 3z^2+6=-4z equation:

Simplifying
3z2 + 6 = -4z

Reorder the terms:
6 + 3z2 = -4z

Solving
6 + 3z2 = -4z

Solving for variable 'z'.

Reorder the terms:
6 + 4z + 3z2 = -4z + 4z

Combine like terms: -4z + 4z = 0
6 + 4z + 3z2 = 0

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

Divide each side by '3'.
2 + 1.333333333z + z2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 1.333333333z + -2 + z2 = 0 + -2

Reorder the terms:
2 + -2 + 1.333333333z + z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 1.333333333z + z2 = 0 + -2
1.333333333z + z2 = 0 + -2

Combine like terms: 0 + -2 = -2
1.333333333z + z2 = -2

The z term is 1.333333333z.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333z + 0.4444444442 + z2 = -2 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333z + z2 = -2 + 0.4444444442

Combine like terms: -2 + 0.4444444442 = -1.5555555558
0.4444444442 + 1.333333333z + z2 = -1.5555555558

Factor a perfect square on the left side:
(z + 0.6666666665)(z + 0.6666666665) = -1.5555555558

Can't calculate square root of the right side.

The solution to this equation could not be determined.