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

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

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

Reorder the terms:
x(-1 + 2x) + -3(2x + -1) = 0
(-1 * x + 2x * x) + -3(2x + -1) = 0
(-1x + 2x2) + -3(2x + -1) = 0

Reorder the terms:
-1x + 2x2 + -3(-1 + 2x) = 0
-1x + 2x2 + (-1 * -3 + 2x * -3) = 0
-1x + 2x2 + (3 + -6x) = 0

Reorder the terms:
3 + -1x + -6x + 2x2 = 0

Combine like terms: -1x + -6x = -7x
3 + -7x + 2x2 = 0

Solving
3 + -7x + 2x2 = 0

Solving for variable 'x'.

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

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

Simplifying
3 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0.5, 3}