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

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

Simplifying
3(2x + -3)(5 + -1x) = 0

Reorder the terms:
3(-3 + 2x)(5 + -1x) = 0

Multiply (-3 + 2x) * (5 + -1x)
3(-3(5 + -1x) + 2x * (5 + -1x)) = 0
3((5 * -3 + -1x * -3) + 2x * (5 + -1x)) = 0
3((-15 + 3x) + 2x * (5 + -1x)) = 0
3(-15 + 3x + (5 * 2x + -1x * 2x)) = 0
3(-15 + 3x + (10x + -2x2)) = 0

Combine like terms: 3x + 10x = 13x
3(-15 + 13x + -2x2) = 0
(-15 * 3 + 13x * 3 + -2x2 * 3) = 0
(-45 + 39x + -6x2) = 0

Solving
-45 + 39x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + 13x + -2x2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 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 + x = 0 + 5

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

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

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {5, 1.5}