3z(z+6)=3z+18z-4

Solution for 3z(z+6)=3z+18z-4 equation:

Simplifying
3z(z + 6) = 3z + 18z + -4

Reorder the terms:
3z(6 + z) = 3z + 18z + -4
(6 * 3z + z * 3z) = 3z + 18z + -4
(18z + 3z2) = 3z + 18z + -4

Reorder the terms:
18z + 3z2 = -4 + 3z + 18z

Combine like terms: 3z + 18z = 21z
18z + 3z2 = -4 + 21z

Solving
18z + 3z2 = -4 + 21z

Solving for variable 'z'.

Reorder the terms:
4 + 18z + -21z + 3z2 = -4 + 21z + 4 + -21z

Combine like terms: 18z + -21z = -3z
4 + -3z + 3z2 = -4 + 21z + 4 + -21z

Reorder the terms:
4 + -3z + 3z2 = -4 + 4 + 21z + -21z

Combine like terms: -4 + 4 = 0
4 + -3z + 3z2 = 0 + 21z + -21z
4 + -3z + 3z2 = 21z + -21z

Combine like terms: 21z + -21z = 0
4 + -3z + 3z2 = 0

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

Divide each side by '3'.
1.333333333 + -1z + z2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -1z + -1.333333333 + z2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -1z + z2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -1z + z2 = 0 + -1.333333333
-1z + z2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-1z + z2 = -1.333333333

The z term is -1z.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1z + 0.25 + z2 = -1.333333333 + 0.25

Reorder the terms:
0.25 + -1z + z2 = -1.333333333 + 0.25

Combine like terms: -1.333333333 + 0.25 = -1.083333333
0.25 + -1z + z2 = -1.083333333

Factor a perfect square on the left side:
(z + -0.5)(z + -0.5) = -1.083333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.