6=z(10-z)

Solution for 6=z(10-z) equation:

Simplifying
6 = z(10 + -1z)
6 = (10 * z + -1z * z)
6 = (10z + -1z2)

Solving
6 = 10z + -1z2

Solving for variable 'z'.

Reorder the terms:
6 + -10z + z2 = 10z + -10z + -1z2 + z2

Combine like terms: 10z + -10z = 0
6 + -10z + z2 = 0 + -1z2 + z2
6 + -10z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
6 + -10z + z2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The z term is -10z.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10z + 25 + z2 = -6 + 25

Reorder the terms:
25 + -10z + z2 = -6 + 25

Combine like terms: -6 + 25 = 19
25 + -10z + z2 = 19

Factor a perfect square on the left side:
(z + -5)(z + -5) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(z + -5) equal to 4.358898944 and -4.358898944.

Subproblem 1
z + -5 = 4.358898944

Simplifying
z + -5 = 4.358898944

Reorder the terms:
-5 + z = 4.358898944

Solving
-5 + z = 4.358898944

Solving for variable 'z'.

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

Add '5' to each side of the equation.
-5 + 5 + z = 4.358898944 + 5

Combine like terms: -5 + 5 = 0
0 + z = 4.358898944 + 5
z = 4.358898944 + 5

Combine like terms: 4.358898944 + 5 = 9.358898944
z = 9.358898944

Simplifying
z = 9.358898944

Subproblem 2
z + -5 = -4.358898944

Simplifying
z + -5 = -4.358898944

Reorder the terms:
-5 + z = -4.358898944

Solving
-5 + z = -4.358898944

Solving for variable 'z'.

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

Add '5' to each side of the equation.
-5 + 5 + z = -4.358898944 + 5

Combine like terms: -5 + 5 = 0
0 + z = -4.358898944 + 5
z = -4.358898944 + 5

Combine like terms: -4.358898944 + 5 = 0.641101056
z = 0.641101056

Simplifying
z = 0.641101056

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {9.358898944, 0.641101056}