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

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

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

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

Multiply (-6 + 5z) * (7 + -1z)
(-6(7 + -1z) + 5z * (7 + -1z)) = 0
((7 * -6 + -1z * -6) + 5z * (7 + -1z)) = 0
((-42 + 6z) + 5z * (7 + -1z)) = 0
(-42 + 6z + (7 * 5z + -1z * 5z)) = 0
(-42 + 6z + (35z + -5z2)) = 0

Combine like terms: 6z + 35z = 41z
(-42 + 41z + -5z2) = 0

Solving
-42 + 41z + -5z2 = 0

Solving for variable 'z'.

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

Subproblem 1
Set the factor '(-7 + z)' equal to zero and attempt to solve:

Simplifying
-7 + z = 0

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

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

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

Simplifying
z = 7
Subproblem 2
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
Solution
z = {7, 1.2}