(4Z-7)(6-Z)=0

Solution for (4Z-7)(6-Z)=0 equation:

Simplifying
(4Z + -7)(6 + -1Z) = 0

Reorder the terms:
(-7 + 4Z)(6 + -1Z) = 0

Multiply (-7 + 4Z) * (6 + -1Z)
(-7(6 + -1Z) + 4Z * (6 + -1Z)) = 0
((6 * -7 + -1Z * -7) + 4Z * (6 + -1Z)) = 0
((-42 + 7Z) + 4Z * (6 + -1Z)) = 0
(-42 + 7Z + (6 * 4Z + -1Z * 4Z)) = 0
(-42 + 7Z + (24Z + -4Z2)) = 0

Combine like terms: 7Z + 24Z = 31Z
(-42 + 31Z + -4Z2) = 0

Solving
-42 + 31Z + -4Z2 = 0

Solving for variable 'Z'.

Factor a trinomial.
(-6 + Z)(7 + -4Z) = 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 + -4Z)' equal to zero and attempt to solve:

Simplifying
7 + -4Z = 0

Solving
7 + -4Z = 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 + -4Z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4Z = 0 + -7
-4Z = 0 + -7

Combine like terms: 0 + -7 = -7
-4Z = -7

Divide each side by '-4'.
Z = 1.75

Simplifying
Z = 1.75
Solution
Z = {6, 1.75}