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

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


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

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

Combine like terms: -3x + -1x = -4x
x(1 + -4x + 3x2) = 0
(1 * x + -4x * x + 3x2 * x) = 0
(1x + -4x2 + 3x3) = 0

Solving
1x + -4x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -4x + 3x2) = 0

Factor a trinomial.
x((1 + -3x)(1 + -1x)) = 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 '(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

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {0, 0.3333333333, 1}

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