3z^2-18z=30

Solution for 3z^2-18z=30 equation:

Simplifying
3z2 + -18z = 30

Reorder the terms:
-18z + 3z2 = 30

Solving
-18z + 3z2 = 30

Solving for variable 'z'.

Reorder the terms:
-30 + -18z + 3z2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -18z + 3z2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + -6z + z2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-10 + -6z + z2)' equal to zero and attempt to solve:

Simplifying
-10 + -6z + z2 = 0

Solving
-10 + -6z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -6z + 10 + z2 = 0 + 10

Reorder the terms:
-10 + 10 + -6z + z2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -6z + z2 = 0 + 10
-6z + z2 = 0 + 10

Combine like terms: 0 + 10 = 10
-6z + z2 = 10

The z term is -6z.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6z + 9 + z2 = 10 + 9

Reorder the terms:
9 + -6z + z2 = 10 + 9

Combine like terms: 10 + 9 = 19
9 + -6z + z2 = 19

Factor a perfect square on the left side:
(z + -3)(z + -3) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(z + -3) equal to 4.358898944 and -4.358898944.

Subproblem 1
z + -3 = 4.358898944

Simplifying
z + -3 = 4.358898944

Reorder the terms:
-3 + z = 4.358898944

Solving
-3 + z = 4.358898944

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + z = 4.358898944 + 3

Combine like terms: -3 + 3 = 0
0 + z = 4.358898944 + 3
z = 4.358898944 + 3

Combine like terms: 4.358898944 + 3 = 7.358898944
z = 7.358898944

Simplifying
z = 7.358898944

Subproblem 2
z + -3 = -4.358898944

Simplifying
z + -3 = -4.358898944

Reorder the terms:
-3 + z = -4.358898944

Solving
-3 + z = -4.358898944

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + z = -4.358898944 + 3

Combine like terms: -3 + 3 = 0
0 + z = -4.358898944 + 3
z = -4.358898944 + 3

Combine like terms: -4.358898944 + 3 = -1.358898944
z = -1.358898944

Simplifying
z = -1.358898944

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {7.358898944, -1.358898944}
Solution
z = {7.358898944, -1.358898944}