2x(x+1)=x+1

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

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

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

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

Solving
2x + 2x2 = 1 + x

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(-1 + -1x)(1 + -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 '(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
Solution
x = {-1, 0.5}