4x-3=x(2x-1)

Solution for 4x-3=x(2x-1) equation:

Simplifying
4x + -3 = x(2x + -1)

Reorder the terms:
-3 + 4x = x(2x + -1)

Reorder the terms:
-3 + 4x = x(-1 + 2x)
-3 + 4x = (-1 * x + 2x * x)
-3 + 4x = (-1x + 2x2)

Solving
-3 + 4x = -1x + 2x2

Solving for variable 'x'.

Combine like terms: 4x + x = 5x
-3 + 5x + -2x2 = -1x + 2x2 + x + -2x2

Reorder the terms:
-3 + 5x + -2x2 = -1x + x + 2x2 + -2x2

Combine like terms: -1x + x = 0
-3 + 5x + -2x2 = 0 + 2x2 + -2x2
-3 + 5x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-3 + 5x + -2x2 = 0

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

Subproblem 1
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
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 = {1.5, 1}