(3z-7)(2-z)=0

Solution for (3z-7)(2-z)=0 equation:

Simplifying
(3z + -7)(2 + -1z) = 0

Reorder the terms:
(-7 + 3z)(2 + -1z) = 0

Multiply (-7 + 3z) * (2 + -1z)
(-7(2 + -1z) + 3z * (2 + -1z)) = 0
((2 * -7 + -1z * -7) + 3z * (2 + -1z)) = 0
((-14 + 7z) + 3z * (2 + -1z)) = 0
(-14 + 7z + (2 * 3z + -1z * 3z)) = 0
(-14 + 7z + (6z + -3z2)) = 0

Combine like terms: 7z + 6z = 13z
(-14 + 13z + -3z2) = 0

Solving
-14 + 13z + -3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-7 + 3z)(2 + -1z) = 0

Subproblem 1
Set the factor '(-7 + 3z)' equal to zero and attempt to solve:

Simplifying
-7 + 3z = 0

Solving
-7 + 3z = 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 + 3z = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 3z = 0 + 7
3z = 0 + 7

Combine like terms: 0 + 7 = 7
3z = 7

Divide each side by '3'.
z = 2.333333333

Simplifying
z = 2.333333333
Subproblem 2
Set the factor '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Solution
z = {2.333333333, 2}