6z+6-1(z+1)(z-1)=8(z-1)

Solution for 6z+6-1(z+1)(z-1)=8(z-1) equation:

Simplifying
6z + 6 + -1(z + 1)(z + -1) = 8(z + -1)

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

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

Multiply (1 + z) * (-1 + z)
6z + 6 + -1(1(-1 + z) + z(-1 + z)) = 8(z + -1)
6z + 6 + -1((-1 * 1 + z * 1) + z(-1 + z)) = 8(z + -1)
6z + 6 + -1((-1 + 1z) + z(-1 + z)) = 8(z + -1)
6z + 6 + -1(-1 + 1z + (-1 * z + z * z)) = 8(z + -1)
6z + 6 + -1(-1 + 1z + (-1z + z2)) = 8(z + -1)

Combine like terms: 1z + -1z = 0
6z + 6 + -1(-1 + 0 + z2) = 8(z + -1)
6z + 6 + -1(-1 + z2) = 8(z + -1)
6z + 6 + (-1 * -1 + z2 * -1) = 8(z + -1)
6z + 6 + (1 + -1z2) = 8(z + -1)

Reorder the terms:
6 + 1 + 6z + -1z2 = 8(z + -1)

Combine like terms: 6 + 1 = 7
7 + 6z + -1z2 = 8(z + -1)

Reorder the terms:
7 + 6z + -1z2 = 8(-1 + z)
7 + 6z + -1z2 = (-1 * 8 + z * 8)
7 + 6z + -1z2 = (-8 + 8z)

Solving
7 + 6z + -1z2 = -8 + 8z

Solving for variable 'z'.

Reorder the terms:
7 + 8 + 6z + -8z + -1z2 = -8 + 8z + 8 + -8z

Combine like terms: 7 + 8 = 15
15 + 6z + -8z + -1z2 = -8 + 8z + 8 + -8z

Combine like terms: 6z + -8z = -2z
15 + -2z + -1z2 = -8 + 8z + 8 + -8z

Reorder the terms:
15 + -2z + -1z2 = -8 + 8 + 8z + -8z

Combine like terms: -8 + 8 = 0
15 + -2z + -1z2 = 0 + 8z + -8z
15 + -2z + -1z2 = 8z + -8z

Combine like terms: 8z + -8z = 0
15 + -2z + -1z2 = 0

Factor a trinomial.
(3 + -1z)(5 + z) = 0

Subproblem 1
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Subproblem 2
Set the factor '(5 + z)' equal to zero and attempt to solve:

Simplifying
5 + z = 0

Solving
5 + z = 0

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

Add '-5' to each side of the equation.
5 + -5 + z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + z = 0 + -5
z = 0 + -5

Combine like terms: 0 + -5 = -5
z = -5

Simplifying
z = -5
Solution
z = {3, -5}