z(2z+3)=-2

Solution for z(2z+3)=-2 equation:

Simplifying
z(2z + 3) = -2

Reorder the terms:
z(3 + 2z) = -2
(3 * z + 2z * z) = -2
(3z + 2z2) = -2

Solving
3z + 2z2 = -2

Solving for variable 'z'.

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

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

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

Divide each side by '2'.
1 + 1.5z + z2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 1.5z + -1 + z2 = 0 + -1

Reorder the terms:
1 + -1 + 1.5z + z2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 1.5z + z2 = 0 + -1
1.5z + z2 = 0 + -1

Combine like terms: 0 + -1 = -1
1.5z + z2 = -1

The z term is 1.5z.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5z + 0.5625 + z2 = -1 + 0.5625

Reorder the terms:
0.5625 + 1.5z + z2 = -1 + 0.5625

Combine like terms: -1 + 0.5625 = -0.4375
0.5625 + 1.5z + z2 = -0.4375

Factor a perfect square on the left side:
(z + 0.75)(z + 0.75) = -0.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.