4(z-4)8z-4=

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Solution for 4(z-4)8z-4= equation: 


Simplifying
4(z + -4) * 8z + -4 = 0

Reorder the terms:
4(-4 + z) * 8z + -4 = 0

Reorder the terms for easier multiplication:
4 * 8z(-4 + z) + -4 = 0

Multiply 4 * 8
32z(-4 + z) + -4 = 0
(-4 * 32z + z * 32z) + -4 = 0
(-128z + 32z2) + -4 = 0

Reorder the terms:
-4 + -128z + 32z2 = 0

Solving
-4 + -128z + 32z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + -32z + 8z2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-1 + -32z + 8z2)' equal to zero and attempt to solve:

Simplifying
-1 + -32z + 8z2 = 0

Solving
-1 + -32z + 8z2 = 0

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

Divide each side by '8'.
-0.125 + -4z + z2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + -4z + 0.125 + z2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + -4z + z2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + -4z + z2 = 0 + 0.125
-4z + z2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
-4z + z2 = 0.125

The z term is -4z.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4z + 4 + z2 = 0.125 + 4

Reorder the terms:
4 + -4z + z2 = 0.125 + 4

Combine like terms: 0.125 + 4 = 4.125
4 + -4z + z2 = 4.125

Factor a perfect square on the left side:
(z + -2)(z + -2) = 4.125

Calculate the square root of the right side: 2.031009601

Break this problem into two subproblems by setting 
(z + -2) equal to 2.031009601 and -2.031009601.


Subproblem 1
z + -2 = 2.031009601

Simplifying
z + -2 = 2.031009601

Reorder the terms:
-2 + z = 2.031009601

Solving
-2 + z = 2.031009601

Solving for variable 'z'.

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

Add '2' to each side of the equation.
-2 + 2 + z = 2.031009601 + 2

Combine like terms: -2 + 2 = 0
0 + z = 2.031009601 + 2
z = 2.031009601 + 2

Combine like terms: 2.031009601 + 2 = 4.031009601
z = 4.031009601

Simplifying
z = 4.031009601


Subproblem 2
z + -2 = -2.031009601

Simplifying
z + -2 = -2.031009601

Reorder the terms:
-2 + z = -2.031009601

Solving
-2 + z = -2.031009601

Solving for variable 'z'.

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

Add '2' to each side of the equation.
-2 + 2 + z = -2.031009601 + 2

Combine like terms: -2 + 2 = 0
0 + z = -2.031009601 + 2
z = -2.031009601 + 2

Combine like terms: -2.031009601 + 2 = -0.031009601
z = -0.031009601

Simplifying
z = -0.031009601


Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {4.031009601, -0.031009601}
Solution
z = {4.031009601, -0.031009601}

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