(x+4)(x+1)=x

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

Simplifying
(x + 4)(x + 1) = x

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

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

Multiply (4 + x) * (1 + x)
(4(1 + x) + x(1 + x)) = x
((1 * 4 + x * 4) + x(1 + x)) = x
((4 + 4x) + x(1 + x)) = x
(4 + 4x + (1 * x + x * x)) = x
(4 + 4x + (1x + x2)) = x

Combine like terms: 4x + 1x = 5x
(4 + 5x + x2) = x

Solving
4 + 5x + x2 = x

Solving for variable 'x'.

Reorder the terms:
4 + 5x + -1x + x2 = x + -1x

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

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

Factor a trinomial.
(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}