2((z-1)(z-1))=20

Solution for 2((z-1)(z-1))=20 equation:

Simplifying
2((z + -1)(z + -1)) = 20

Reorder the terms:
2((-1 + z)(z + -1)) = 20

Reorder the terms:
2((-1 + z)(-1 + z)) = 20

Multiply (-1 + z) * (-1 + z)
2((-1(-1 + z) + z(-1 + z))) = 20
2(((-1 * -1 + z * -1) + z(-1 + z))) = 20
2(((1 + -1z) + z(-1 + z))) = 20
2((1 + -1z + (-1 * z + z * z))) = 20
2((1 + -1z + (-1z + z2))) = 20

Combine like terms: -1z + -1z = -2z
2((1 + -2z + z2)) = 20
(1 * 2 + -2z * 2 + z2 * 2) = 20
(2 + -4z + 2z2) = 20

Solving
2 + -4z + 2z2 = 20

Solving for variable 'z'.

Reorder the terms:
2 + -20 + -4z + 2z2 = 20 + -20

Combine like terms: 2 + -20 = -18
-18 + -4z + 2z2 = 20 + -20

Combine like terms: 20 + -20 = 0
-18 + -4z + 2z2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -2z + z2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + -2z + z2)' equal to zero and attempt to solve:

Simplifying
-9 + -2z + z2 = 0

Solving
-9 + -2z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -2z + 9 + z2 = 0 + 9

Reorder the terms:
-9 + 9 + -2z + z2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2z + z2 = 0 + 9
-2z + z2 = 0 + 9

Combine like terms: 0 + 9 = 9
-2z + z2 = 9

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 = 9 + 1

Reorder the terms:
1 + -2z + z2 = 9 + 1

Combine like terms: 9 + 1 = 10
1 + -2z + z2 = 10

Factor a perfect square on the left side:
(z + -1)(z + -1) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(z + -1) equal to 3.16227766 and -3.16227766.

Subproblem 1
z + -1 = 3.16227766

Simplifying
z + -1 = 3.16227766

Reorder the terms:
-1 + z = 3.16227766

Solving
-1 + z = 3.16227766

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 = 3.16227766 + 1

Combine like terms: -1 + 1 = 0
0 + z = 3.16227766 + 1
z = 3.16227766 + 1

Combine like terms: 3.16227766 + 1 = 4.16227766
z = 4.16227766

Simplifying
z = 4.16227766

Subproblem 2
z + -1 = -3.16227766

Simplifying
z + -1 = -3.16227766

Reorder the terms:
-1 + z = -3.16227766

Solving
-1 + z = -3.16227766

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 = -3.16227766 + 1

Combine like terms: -1 + 1 = 0
0 + z = -3.16227766 + 1
z = -3.16227766 + 1

Combine like terms: -3.16227766 + 1 = -2.16227766
z = -2.16227766

Simplifying
z = -2.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {4.16227766, -2.16227766}
Solution
z = {4.16227766, -2.16227766}