5z^2+3=-3z

Solution for 5z^2+3=-3z equation:

Simplifying
5z2 + 3 = -3z

Reorder the terms:
3 + 5z2 = -3z

Solving
3 + 5z2 = -3z

Solving for variable 'z'.

Reorder the terms:
3 + 3z + 5z2 = -3z + 3z

Combine like terms: -3z + 3z = 0
3 + 3z + 5z2 = 0

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

Divide each side by '5'.
0.6 + 0.6z + z2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + 0.6z + -0.6 + z2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + 0.6z + z2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + 0.6z + z2 = 0 + -0.6
0.6z + z2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
0.6z + z2 = -0.6

The z term is 0.6z.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6z + 0.09 + z2 = -0.6 + 0.09

Reorder the terms:
0.09 + 0.6z + z2 = -0.6 + 0.09

Combine like terms: -0.6 + 0.09 = -0.51
0.09 + 0.6z + z2 = -0.51

Factor a perfect square on the left side:
(z + 0.3)(z + 0.3) = -0.51

Can't calculate square root of the right side.

The solution to this equation could not be determined.