6(z+2)=5(z-6)z

Solution for 6(z+2)=5(z-6)z equation:

Simplifying
6(z + 2) = 5(z + -6) * z

Reorder the terms:
6(2 + z) = 5(z + -6) * z
(2 * 6 + z * 6) = 5(z + -6) * z
(12 + 6z) = 5(z + -6) * z

Reorder the terms:
12 + 6z = 5(-6 + z) * z

Reorder the terms for easier multiplication:
12 + 6z = 5z(-6 + z)
12 + 6z = (-6 * 5z + z * 5z)
12 + 6z = (-30z + 5z2)

Solving
12 + 6z = -30z + 5z2

Solving for variable 'z'.

Combine like terms: 6z + 30z = 36z
12 + 36z + -5z2 = -30z + 5z2 + 30z + -5z2

Reorder the terms:
12 + 36z + -5z2 = -30z + 30z + 5z2 + -5z2

Combine like terms: -30z + 30z = 0
12 + 36z + -5z2 = 0 + 5z2 + -5z2
12 + 36z + -5z2 = 5z2 + -5z2

Combine like terms: 5z2 + -5z2 = 0
12 + 36z + -5z2 = 0

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

Divide each side by '-5'.
-2.4 + -7.2z + z2 = 0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + -7.2z + 2.4 + z2 = 0 + 2.4

Reorder the terms:
-2.4 + 2.4 + -7.2z + z2 = 0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + -7.2z + z2 = 0 + 2.4
-7.2z + z2 = 0 + 2.4

Combine like terms: 0 + 2.4 = 2.4
-7.2z + z2 = 2.4

The z term is -7.2z.  Take half its coefficient (-3.6).
Square it (12.96) and add it to both sides.

Add '12.96' to each side of the equation.
-7.2z + 12.96 + z2 = 2.4 + 12.96

Reorder the terms:
12.96 + -7.2z + z2 = 2.4 + 12.96

Combine like terms: 2.4 + 12.96 = 15.36
12.96 + -7.2z + z2 = 15.36

Factor a perfect square on the left side:
(z + -3.6)(z + -3.6) = 15.36

Calculate the square root of the right side: 3.919183588

Break this problem into two subproblems by setting 
(z + -3.6) equal to 3.919183588 and -3.919183588.

Subproblem 1
z + -3.6 = 3.919183588

Simplifying
z + -3.6 = 3.919183588

Reorder the terms:
-3.6 + z = 3.919183588

Solving
-3.6 + z = 3.919183588

Solving for variable 'z'.

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

Add '3.6' to each side of the equation.
-3.6 + 3.6 + z = 3.919183588 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + z = 3.919183588 + 3.6
z = 3.919183588 + 3.6

Combine like terms: 3.919183588 + 3.6 = 7.519183588
z = 7.519183588

Simplifying
z = 7.519183588

Subproblem 2
z + -3.6 = -3.919183588

Simplifying
z + -3.6 = -3.919183588

Reorder the terms:
-3.6 + z = -3.919183588

Solving
-3.6 + z = -3.919183588

Solving for variable 'z'.

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

Add '3.6' to each side of the equation.
-3.6 + 3.6 + z = -3.919183588 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + z = -3.919183588 + 3.6
z = -3.919183588 + 3.6

Combine like terms: -3.919183588 + 3.6 = -0.319183588
z = -0.319183588

Simplifying
z = -0.319183588

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {7.519183588, -0.319183588}