x(2x+1)=x

Solution for x(2x+1)=x equation:

Simplifying
x(2x + 1) = x

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

Solving
1x + 2x2 = x

Solving for variable 'x'.

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

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

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

Ignore the factor 2.
Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Solution
x = {0}