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

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

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

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

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

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

Combine like terms: -1x + -2x = -3x
3(1 + -3x + 2x2) = 0
(1 * 3 + -3x * 3 + 2x2 * 3) = 0
(3 + -9x + 6x2) = 0

Solving
3 + -9x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -3x + 2x2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Subproblem 2
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 = {0.5, 1}