(1z-6)(-7z-5)=0

Solution for (1z-6)(-7z-5)=0 equation:

Simplifying
(1z + -6)(-7z + -5) = 0

Reorder the terms:
(-6 + 1z)(-7z + -5) = 0

Reorder the terms:
(-6 + 1z)(-5 + -7z) = 0

Multiply (-6 + 1z) * (-5 + -7z)
(-6(-5 + -7z) + 1z * (-5 + -7z)) = 0
((-5 * -6 + -7z * -6) + 1z * (-5 + -7z)) = 0
((30 + 42z) + 1z * (-5 + -7z)) = 0
(30 + 42z + (-5 * 1z + -7z * 1z)) = 0
(30 + 42z + (-5z + -7z2)) = 0

Combine like terms: 42z + -5z = 37z
(30 + 37z + -7z2) = 0

Solving
30 + 37z + -7z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(6 + -1z)(5 + 7z) = 0

Subproblem 1
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z = 0 + -6
-1z = 0 + -6

Combine like terms: 0 + -6 = -6
-1z = -6

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Subproblem 2
Set the factor '(5 + 7z)' equal to zero and attempt to solve:

Simplifying
5 + 7z = 0

Solving
5 + 7z = 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 + 7z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 7z = 0 + -5
7z = 0 + -5

Combine like terms: 0 + -5 = -5
7z = -5

Divide each side by '7'.
z = -0.7142857143

Simplifying
z = -0.7142857143
Solution
z = {6, -0.7142857143}