(3-z)(5z-9)=0

Solution for (3-z)(5z-9)=0 equation:

Simplifying
(3 + -1z)(5z + -9) = 0

Reorder the terms:
(3 + -1z)(-9 + 5z) = 0

Multiply (3 + -1z) * (-9 + 5z)
(3(-9 + 5z) + -1z * (-9 + 5z)) = 0
((-9 * 3 + 5z * 3) + -1z * (-9 + 5z)) = 0
((-27 + 15z) + -1z * (-9 + 5z)) = 0
(-27 + 15z + (-9 * -1z + 5z * -1z)) = 0
(-27 + 15z + (9z + -5z2)) = 0

Combine like terms: 15z + 9z = 24z
(-27 + 24z + -5z2) = 0

Solving
-27 + 24z + -5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-3 + z)(9 + -5z) = 0

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

Simplifying
-3 + z = 0

Solving
-3 + z = 0

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

Add '3' to each side of the equation.
-3 + 3 + z = 0 + 3

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

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

Simplifying
z = 3
Subproblem 2
Set the factor '(9 + -5z)' equal to zero and attempt to solve:

Simplifying
9 + -5z = 0

Solving
9 + -5z = 0

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

Add '-9' to each side of the equation.
9 + -9 + -5z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5z = 0 + -9
-5z = 0 + -9

Combine like terms: 0 + -9 = -9
-5z = -9

Divide each side by '-5'.
z = 1.8

Simplifying
z = 1.8
Solution
z = {3, 1.8}