x(x+1)=x+4

Solution for x(x+1)=x+4 equation:

Simplifying
x(x + 1) = x + 4

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

Reorder the terms:
1x + x2 = 4 + x

Solving
1x + x2 = 4 + x

Solving for variable 'x'.

Reorder the terms:
-4 + 1x + -1x + x2 = 4 + x + -4 + -1x

Combine like terms: 1x + -1x = 0
-4 + 0 + x2 = 4 + x + -4 + -1x
-4 + x2 = 4 + x + -4 + -1x

Reorder the terms:
-4 + x2 = 4 + -4 + x + -1x

Combine like terms: 4 + -4 = 0
-4 + x2 = 0 + x + -1x
-4 + x2 = x + -1x

Combine like terms: x + -1x = 0
-4 + x2 = 0

Factor a difference between two squares.
(2 + x)(-2 + x) = 0

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

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

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

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

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

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

Simplifying
x = 2
Solution
x = {-2, 2}