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

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

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

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

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

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

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

Solving for variable 'x'.

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

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

Simplifying
-1 + x = 0

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

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

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

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