5z^2+z=3z-6

Solution for 5z^2+z=3z-6 equation:

Simplifying
5z2 + z = 3z + -6

Reorder the terms:
z + 5z2 = 3z + -6

Reorder the terms:
z + 5z2 = -6 + 3z

Solving
z + 5z2 = -6 + 3z

Solving for variable 'z'.

Reorder the terms:
6 + z + -3z + 5z2 = -6 + 3z + 6 + -3z

Combine like terms: z + -3z = -2z
6 + -2z + 5z2 = -6 + 3z + 6 + -3z

Reorder the terms:
6 + -2z + 5z2 = -6 + 6 + 3z + -3z

Combine like terms: -6 + 6 = 0
6 + -2z + 5z2 = 0 + 3z + -3z
6 + -2z + 5z2 = 3z + -3z

Combine like terms: 3z + -3z = 0
6 + -2z + 5z2 = 0

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

Divide each side by '5'.
1.2 + -0.4z + z2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + -0.4z + -1.2 + z2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + -0.4z + z2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + -0.4z + z2 = 0 + -1.2
-0.4z + z2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
-0.4z + z2 = -1.2

The z term is -0.4z.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4z + 0.04 + z2 = -1.2 + 0.04

Reorder the terms:
0.04 + -0.4z + z2 = -1.2 + 0.04

Combine like terms: -1.2 + 0.04 = -1.16
0.04 + -0.4z + z2 = -1.16

Factor a perfect square on the left side:
(z + -0.2)(z + -0.2) = -1.16

Can't calculate square root of the right side.

The solution to this equation could not be determined.