(3x-9)(5-2x)=0

Solution for (3x-9)(5-2x)=0 equation:

Simplifying
(3x + -9)(5 + -2x) = 0

Reorder the terms:
(-9 + 3x)(5 + -2x) = 0

Multiply (-9 + 3x) * (5 + -2x)
(-9(5 + -2x) + 3x * (5 + -2x)) = 0
((5 * -9 + -2x * -9) + 3x * (5 + -2x)) = 0
((-45 + 18x) + 3x * (5 + -2x)) = 0
(-45 + 18x + (5 * 3x + -2x * 3x)) = 0
(-45 + 18x + (15x + -6x2)) = 0

Combine like terms: 18x + 15x = 33x
(-45 + 33x + -6x2) = 0

Solving
-45 + 33x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + 11x + -2x2) = 0

Factor a trinomial.
3((-3 + x)(5 + -2x)) = 0

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

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

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

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

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

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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {3, 2.5}