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

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

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

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

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

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

Solving
-42 + 37z + -5z2 = 0

Solving for variable 'z'.

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

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

Simplifying
-6 + z = 0

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

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

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

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

Simplifying
7 + -5z = 0

Solving
7 + -5z = 0

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

Add '-7' to each side of the equation.
7 + -7 + -5z = 0 + -7

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

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

Divide each side by '-5'.
z = 1.4

Simplifying
z = 1.4
Solution
z = {6, 1.4}