5(6z-1)-z(z+6)=5(z+1)

Solution for 5(6z-1)-z(z+6)=5(z+1) equation:

Simplifying
5(6z + -1) + -1z(z + 6) = 5(z + 1)

Reorder the terms:
5(-1 + 6z) + -1z(z + 6) = 5(z + 1)
(-1 * 5 + 6z * 5) + -1z(z + 6) = 5(z + 1)
(-5 + 30z) + -1z(z + 6) = 5(z + 1)

Reorder the terms:
-5 + 30z + -1z(6 + z) = 5(z + 1)
-5 + 30z + (6 * -1z + z * -1z) = 5(z + 1)
-5 + 30z + (-6z + -1z2) = 5(z + 1)

Combine like terms: 30z + -6z = 24z
-5 + 24z + -1z2 = 5(z + 1)

Reorder the terms:
-5 + 24z + -1z2 = 5(1 + z)
-5 + 24z + -1z2 = (1 * 5 + z * 5)
-5 + 24z + -1z2 = (5 + 5z)

Solving
-5 + 24z + -1z2 = 5 + 5z

Solving for variable 'z'.

Reorder the terms:
-5 + -5 + 24z + -5z + -1z2 = 5 + 5z + -5 + -5z

Combine like terms: -5 + -5 = -10
-10 + 24z + -5z + -1z2 = 5 + 5z + -5 + -5z

Combine like terms: 24z + -5z = 19z
-10 + 19z + -1z2 = 5 + 5z + -5 + -5z

Reorder the terms:
-10 + 19z + -1z2 = 5 + -5 + 5z + -5z

Combine like terms: 5 + -5 = 0
-10 + 19z + -1z2 = 0 + 5z + -5z
-10 + 19z + -1z2 = 5z + -5z

Combine like terms: 5z + -5z = 0
-10 + 19z + -1z2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
10 + -19z + z2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -19z + -10 + z2 = 0 + -10

Reorder the terms:
10 + -10 + -19z + z2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -19z + z2 = 0 + -10
-19z + z2 = 0 + -10

Combine like terms: 0 + -10 = -10
-19z + z2 = -10

The z term is -19z.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19z + 90.25 + z2 = -10 + 90.25

Reorder the terms:
90.25 + -19z + z2 = -10 + 90.25

Combine like terms: -10 + 90.25 = 80.25
90.25 + -19z + z2 = 80.25

Factor a perfect square on the left side:
(z + -9.5)(z + -9.5) = 80.25

Calculate the square root of the right side: 8.958236434

Break this problem into two subproblems by setting 
(z + -9.5) equal to 8.958236434 and -8.958236434.

Subproblem 1
z + -9.5 = 8.958236434

Simplifying
z + -9.5 = 8.958236434

Reorder the terms:
-9.5 + z = 8.958236434

Solving
-9.5 + z = 8.958236434

Solving for variable 'z'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + z = 8.958236434 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + z = 8.958236434 + 9.5
z = 8.958236434 + 9.5

Combine like terms: 8.958236434 + 9.5 = 18.458236434
z = 18.458236434

Simplifying
z = 18.458236434

Subproblem 2
z + -9.5 = -8.958236434

Simplifying
z + -9.5 = -8.958236434

Reorder the terms:
-9.5 + z = -8.958236434

Solving
-9.5 + z = -8.958236434

Solving for variable 'z'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + z = -8.958236434 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + z = -8.958236434 + 9.5
z = -8.958236434 + 9.5

Combine like terms: -8.958236434 + 9.5 = 0.541763566
z = 0.541763566

Simplifying
z = 0.541763566

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {18.458236434, 0.541763566}