x(2x-1)=3

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

Simplifying
x(2x + -1) = 3

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

Solving
-1x + 2x2 = 3

Solving for variable 'x'.

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

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

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

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-1, 1.5}