-(6z+2)(2-8z)+(-7z-6)(2-2z)=

Solution for -(6z+2)(2-8z)+(-7z-6)(2-2z)= equation:

Simplifying
-1(6z + 2)(2 + -8z) + (-7z + -6)(2 + -2z) = 0

Reorder the terms:
-1(2 + 6z)(2 + -8z) + (-7z + -6)(2 + -2z) = 0

Multiply (2 + 6z) * (2 + -8z)
-1(2(2 + -8z) + 6z * (2 + -8z)) + (-7z + -6)(2 + -2z) = 0
-1((2 * 2 + -8z * 2) + 6z * (2 + -8z)) + (-7z + -6)(2 + -2z) = 0
-1((4 + -16z) + 6z * (2 + -8z)) + (-7z + -6)(2 + -2z) = 0
-1(4 + -16z + (2 * 6z + -8z * 6z)) + (-7z + -6)(2 + -2z) = 0
-1(4 + -16z + (12z + -48z2)) + (-7z + -6)(2 + -2z) = 0

Combine like terms: -16z + 12z = -4z
-1(4 + -4z + -48z2) + (-7z + -6)(2 + -2z) = 0
(4 * -1 + -4z * -1 + -48z2 * -1) + (-7z + -6)(2 + -2z) = 0
(-4 + 4z + 48z2) + (-7z + -6)(2 + -2z) = 0

Reorder the terms:
-4 + 4z + 48z2 + (-6 + -7z)(2 + -2z) = 0

Multiply (-6 + -7z) * (2 + -2z)
-4 + 4z + 48z2 + (-6(2 + -2z) + -7z * (2 + -2z)) = 0
-4 + 4z + 48z2 + ((2 * -6 + -2z * -6) + -7z * (2 + -2z)) = 0
-4 + 4z + 48z2 + ((-12 + 12z) + -7z * (2 + -2z)) = 0
-4 + 4z + 48z2 + (-12 + 12z + (2 * -7z + -2z * -7z)) = 0
-4 + 4z + 48z2 + (-12 + 12z + (-14z + 14z2)) = 0

Combine like terms: 12z + -14z = -2z
-4 + 4z + 48z2 + (-12 + -2z + 14z2) = 0

Reorder the terms:
-4 + -12 + 4z + -2z + 48z2 + 14z2 = 0

Combine like terms: -4 + -12 = -16
-16 + 4z + -2z + 48z2 + 14z2 = 0

Combine like terms: 4z + -2z = 2z
-16 + 2z + 48z2 + 14z2 = 0

Combine like terms: 48z2 + 14z2 = 62z2
-16 + 2z + 62z2 = 0

Solving
-16 + 2z + 62z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + z + 31z2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + z + 31z2)' equal to zero and attempt to solve:

Simplifying
-8 + z + 31z2 = 0

Solving
-8 + z + 31z2 = 0

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

Divide each side by '31'.
-0.2580645161 + 0.03225806452z + z2 = 0

Move the constant term to the right:

Add '0.2580645161' to each side of the equation.
-0.2580645161 + 0.03225806452z + 0.2580645161 + z2 = 0 + 0.2580645161

Reorder the terms:
-0.2580645161 + 0.2580645161 + 0.03225806452z + z2 = 0 + 0.2580645161

Combine like terms: -0.2580645161 + 0.2580645161 = 0.0000000000
0.0000000000 + 0.03225806452z + z2 = 0 + 0.2580645161
0.03225806452z + z2 = 0 + 0.2580645161

Combine like terms: 0 + 0.2580645161 = 0.2580645161
0.03225806452z + z2 = 0.2580645161

The z term is z.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.03225806452z + 0.25 + z2 = 0.2580645161 + 0.25

Reorder the terms:
0.25 + 0.03225806452z + z2 = 0.2580645161 + 0.25

Combine like terms: 0.2580645161 + 0.25 = 0.5080645161
0.25 + 0.03225806452z + z2 = 0.5080645161

Factor a perfect square on the left side:
(z + 0.5)(z + 0.5) = 0.5080645161

Calculate the square root of the right side: 0.712786445

Break this problem into two subproblems by setting 
(z + 0.5) equal to 0.712786445 and -0.712786445.

Subproblem 1
z + 0.5 = 0.712786445

Simplifying
z + 0.5 = 0.712786445

Reorder the terms:
0.5 + z = 0.712786445

Solving
0.5 + z = 0.712786445

Solving for variable 'z'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + z = 0.712786445 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + z = 0.712786445 + -0.5
z = 0.712786445 + -0.5

Combine like terms: 0.712786445 + -0.5 = 0.212786445
z = 0.212786445

Simplifying
z = 0.212786445

Subproblem 2
z + 0.5 = -0.712786445

Simplifying
z + 0.5 = -0.712786445

Reorder the terms:
0.5 + z = -0.712786445

Solving
0.5 + z = -0.712786445

Solving for variable 'z'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + z = -0.712786445 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + z = -0.712786445 + -0.5
z = -0.712786445 + -0.5

Combine like terms: -0.712786445 + -0.5 = -1.212786445
z = -1.212786445

Simplifying
z = -1.212786445

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {0.212786445, -1.212786445}
Solution
z = {0.212786445, -1.212786445}