z(4-z)-2(z-3)=

Solution for z(4-z)-2(z-3)= equation:

Simplifying
z(4 + -1z) + -2(z + -3) = 0
(4 * z + -1z * z) + -2(z + -3) = 0
(4z + -1z2) + -2(z + -3) = 0

Reorder the terms:
4z + -1z2 + -2(-3 + z) = 0
4z + -1z2 + (-3 * -2 + z * -2) = 0
4z + -1z2 + (6 + -2z) = 0

Reorder the terms:
6 + 4z + -2z + -1z2 = 0

Combine like terms: 4z + -2z = 2z
6 + 2z + -1z2 = 0

Solving
6 + 2z + -1z2 = 0

Solving for variable 'z'.

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

Divide each side by '-1'.
-6 + -2z + z2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -2z + 6 + z2 = 0 + 6

Reorder the terms:
-6 + 6 + -2z + z2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -2z + z2 = 0 + 6
-2z + z2 = 0 + 6

Combine like terms: 0 + 6 = 6
-2z + z2 = 6

The z term is -2z.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2z + 1 + z2 = 6 + 1

Reorder the terms:
1 + -2z + z2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + -2z + z2 = 7

Factor a perfect square on the left side:
(z + -1)(z + -1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(z + -1) equal to 2.645751311 and -2.645751311.

Subproblem 1
z + -1 = 2.645751311

Simplifying
z + -1 = 2.645751311

Reorder the terms:
-1 + z = 2.645751311

Solving
-1 + z = 2.645751311

Solving for variable 'z'.

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

Add '1' to each side of the equation.
-1 + 1 + z = 2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + z = 2.645751311 + 1
z = 2.645751311 + 1

Combine like terms: 2.645751311 + 1 = 3.645751311
z = 3.645751311

Simplifying
z = 3.645751311

Subproblem 2
z + -1 = -2.645751311

Simplifying
z + -1 = -2.645751311

Reorder the terms:
-1 + z = -2.645751311

Solving
-1 + z = -2.645751311

Solving for variable 'z'.

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

Add '1' to each side of the equation.
-1 + 1 + z = -2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + z = -2.645751311 + 1
z = -2.645751311 + 1

Combine like terms: -2.645751311 + 1 = -1.645751311
z = -1.645751311

Simplifying
z = -1.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {3.645751311, -1.645751311}