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

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


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

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

Multiply (2 + -1x) * (-3 + 5x)
x(2(-3 + 5x) + -1x * (-3 + 5x)) = 0
x((-3 * 2 + 5x * 2) + -1x * (-3 + 5x)) = 0
x((-6 + 10x) + -1x * (-3 + 5x)) = 0
x(-6 + 10x + (-3 * -1x + 5x * -1x)) = 0
x(-6 + 10x + (3x + -5x2)) = 0

Combine like terms: 10x + 3x = 13x
x(-6 + 13x + -5x2) = 0
(-6 * x + 13x * x + -5x2 * x) = 0
(-6x + 13x2 + -5x3) = 0

Solving
-6x + 13x2 + -5x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-6 + 13x + -5x2) = 0

Factor a trinomial.
x((-2 + x)(3 + -5x)) = 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 '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

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

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

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

Simplifying
x = 2

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

Simplifying
3 + -5x = 0

Solving
3 + -5x = 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 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {0, 2, 0.6}

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