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

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Solution for (3x-1)(2-x)5x=0 equation: 


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

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

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

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

Combine like terms: 1x + 6x = 7x
5x(-2 + 7x + -3x2) = 0
(-2 * 5x + 7x * 5x + -3x2 * 5x) = 0
(-10x + 35x2 + -15x3) = 0

Solving
-10x + 35x2 + -15x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-2 + 7x + -3x2) = 0

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

Ignore the factor 5.

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 '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3x = 0 + -1

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {0, 2, 0.3333333333}

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