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

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

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

Multiply (3 + -1x) * (5 + -2x)
2x(3(5 + -2x) + -1x * (5 + -2x)) = 0
2x((5 * 3 + -2x * 3) + -1x * (5 + -2x)) = 0
2x((15 + -6x) + -1x * (5 + -2x)) = 0
2x(15 + -6x + (5 * -1x + -2x * -1x)) = 0
2x(15 + -6x + (-5x + 2x2)) = 0

Combine like terms: -6x + -5x = -11x
2x(15 + -11x + 2x2) = 0
(15 * 2x + -11x * 2x + 2x2 * 2x) = 0
(30x + -22x2 + 4x3) = 0

Solving
30x + -22x2 + 4x3 = 0

Solving for variable 'x'.

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

Factor a trinomial.
2x((5 + -2x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
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
Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, 2.5, 3}