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

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

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

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

Reorder the terms:
18z + 3z2 = -6 + 3z + 18z

Combine like terms: 3z + 18z = 21z
18z + 3z2 = -6 + 21z

Solving
18z + 3z2 = -6 + 21z

Solving for variable 'z'.

Reorder the terms:
6 + 18z + -21z + 3z2 = -6 + 21z + 6 + -21z

Combine like terms: 18z + -21z = -3z
6 + -3z + 3z2 = -6 + 21z + 6 + -21z

Reorder the terms:
6 + -3z + 3z2 = -6 + 6 + 21z + -21z

Combine like terms: -6 + 6 = 0
6 + -3z + 3z2 = 0 + 21z + -21z
6 + -3z + 3z2 = 21z + -21z

Combine like terms: 21z + -21z = 0
6 + -3z + 3z2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -1z + z2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -1z + z2)' equal to zero and attempt to solve:

Simplifying
2 + -1z + z2 = 0

Solving
2 + -1z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -1z + -2 + z2 = 0 + -2

Reorder the terms:
2 + -2 + -1z + z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z + z2 = 0 + -2
-1z + z2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1z + z2 = -2

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 = -2 + 0.25

Reorder the terms:
0.25 + -1z + z2 = -2 + 0.25

Combine like terms: -2 + 0.25 = -1.75
0.25 + -1z + z2 = -1.75

Factor a perfect square on the left side:
(z + -0.5)(z + -0.5) = -1.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.