(4z-2)(4-5z)-(z-4)=

Solution for (4z-2)(4-5z)-(z-4)= equation:

Simplifying
(4z + -2)(4 + -5z) + -1(z + -4) = 0

Reorder the terms:
(-2 + 4z)(4 + -5z) + -1(z + -4) = 0

Multiply (-2 + 4z) * (4 + -5z)
(-2(4 + -5z) + 4z * (4 + -5z)) + -1(z + -4) = 0
((4 * -2 + -5z * -2) + 4z * (4 + -5z)) + -1(z + -4) = 0
((-8 + 10z) + 4z * (4 + -5z)) + -1(z + -4) = 0
(-8 + 10z + (4 * 4z + -5z * 4z)) + -1(z + -4) = 0
(-8 + 10z + (16z + -20z2)) + -1(z + -4) = 0

Combine like terms: 10z + 16z = 26z
(-8 + 26z + -20z2) + -1(z + -4) = 0

Reorder the terms:
-8 + 26z + -20z2 + -1(-4 + z) = 0
-8 + 26z + -20z2 + (-4 * -1 + z * -1) = 0
-8 + 26z + -20z2 + (4 + -1z) = 0

Reorder the terms:
-8 + 4 + 26z + -1z + -20z2 = 0

Combine like terms: -8 + 4 = -4
-4 + 26z + -1z + -20z2 = 0

Combine like terms: 26z + -1z = 25z
-4 + 25z + -20z2 = 0

Solving
-4 + 25z + -20z2 = 0

Solving for variable 'z'.

Begin completing the square.  Divide all terms by
-20 the coefficient of the squared term: 

Divide each side by '-20'.
0.2 + -1.25z + z2 = 0.0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -1.25z + -0.2 + z2 = 0.0 + -0.2

Reorder the terms:
0.2 + -0.2 + -1.25z + z2 = 0.0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -1.25z + z2 = 0.0 + -0.2
-1.25z + z2 = 0.0 + -0.2

Combine like terms: 0.0 + -0.2 = -0.2
-1.25z + z2 = -0.2

The z term is -1.25z.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25z + 0.390625 + z2 = -0.2 + 0.390625

Reorder the terms:
0.390625 + -1.25z + z2 = -0.2 + 0.390625

Combine like terms: -0.2 + 0.390625 = 0.190625
0.390625 + -1.25z + z2 = 0.190625

Factor a perfect square on the left side:
(z + -0.625)(z + -0.625) = 0.190625

Calculate the square root of the right side: 0.43660623

Break this problem into two subproblems by setting 
(z + -0.625) equal to 0.43660623 and -0.43660623.

Subproblem 1
z + -0.625 = 0.43660623

Simplifying
z + -0.625 = 0.43660623

Reorder the terms:
-0.625 + z = 0.43660623

Solving
-0.625 + z = 0.43660623

Solving for variable 'z'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + z = 0.43660623 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + z = 0.43660623 + 0.625
z = 0.43660623 + 0.625

Combine like terms: 0.43660623 + 0.625 = 1.06160623
z = 1.06160623

Simplifying
z = 1.06160623

Subproblem 2
z + -0.625 = -0.43660623

Simplifying
z + -0.625 = -0.43660623

Reorder the terms:
-0.625 + z = -0.43660623

Solving
-0.625 + z = -0.43660623

Solving for variable 'z'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + z = -0.43660623 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + z = -0.43660623 + 0.625
z = -0.43660623 + 0.625

Combine like terms: -0.43660623 + 0.625 = 0.18839377
z = 0.18839377

Simplifying
z = 0.18839377

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {1.06160623, 0.18839377}