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

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


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

Multiply (3 + -2x) * (5 + -2x)
x(3(5 + -2x) + -2x * (5 + -2x)) = 0
x((5 * 3 + -2x * 3) + -2x * (5 + -2x)) = 0
x((15 + -6x) + -2x * (5 + -2x)) = 0
x(15 + -6x + (5 * -2x + -2x * -2x)) = 0
x(15 + -6x + (-10x + 4x2)) = 0

Combine like terms: -6x + -10x = -16x
x(15 + -16x + 4x2) = 0
(15 * x + -16x * x + 4x2 * x) = 0
(15x + -16x2 + 4x3) = 0

Solving
15x + -16x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(15 + -16x + 4x2) = 0

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


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 '(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

Subproblem 3
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 = {0, 1.5, 2.5}

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