2x+1=2x(x+1)

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

Simplifying
2x + 1 = 2x(x + 1)

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

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

Add '-2x' to each side of the equation.
1 + 2x + -2x = 2x + -2x + 2x2

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

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

Solving
1 = 2x2

Solving for variable 'x'.

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

Add '-2x2' to each side of the equation.
1 + -2x2 = 2x2 + -2x2

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

Add '-1' to each side of the equation.
1 + -1 + -2x2 = 0 + -1

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

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

Divide each side by '-2'.
x2 = 0.5

Simplifying
x2 = 0.5

Take the square root of each side:
x = {-0.707106781, 0.707106781}