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

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

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

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

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

Combine like terms: 5z + 6z = 11z
(-6 + 11z + -5z2) = 0

Solving
-6 + 11z + -5z2 = 0

Solving for variable 'z'.

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

Subproblem 1
Set the factor '(-6 + 5z)' equal to zero and attempt to solve:

Simplifying
-6 + 5z = 0

Solving
-6 + 5z = 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 + 5z = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 5z = 0 + 6
5z = 0 + 6

Combine like terms: 0 + 6 = 6
5z = 6

Divide each side by '5'.
z = 1.2

Simplifying
z = 1.2
Subproblem 2
Set the factor '(1 + -1z)' equal to zero and attempt to solve:

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

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

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

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

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

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

Simplifying
z = 1
Solution
z = {1.2, 1}