(x+2)(x+1)=x+5

Solution for (x+2)(x+1)=x+5 equation:

Simplifying
(x + 2)(x + 1) = x + 5

Reorder the terms:
(2 + x)(x + 1) = x + 5

Reorder the terms:
(2 + x)(1 + x) = x + 5

Multiply (2 + x) * (1 + x)
(2(1 + x) + x(1 + x)) = x + 5
((1 * 2 + x * 2) + x(1 + x)) = x + 5
((2 + 2x) + x(1 + x)) = x + 5
(2 + 2x + (1 * x + x * x)) = x + 5
(2 + 2x + (1x + x2)) = x + 5

Combine like terms: 2x + 1x = 3x
(2 + 3x + x2) = x + 5

Reorder the terms:
2 + 3x + x2 = 5 + x

Solving
2 + 3x + x2 = 5 + x

Solving for variable 'x'.

Reorder the terms:
2 + -5 + 3x + -1x + x2 = 5 + x + -5 + -1x

Combine like terms: 2 + -5 = -3
-3 + 3x + -1x + x2 = 5 + x + -5 + -1x

Combine like terms: 3x + -1x = 2x
-3 + 2x + x2 = 5 + x + -5 + -1x

Reorder the terms:
-3 + 2x + x2 = 5 + -5 + x + -1x

Combine like terms: 5 + -5 = 0
-3 + 2x + x2 = 0 + x + -1x
-3 + 2x + x2 = x + -1x

Combine like terms: x + -1x = 0
-3 + 2x + x2 = 0

Factor a trinomial.
(-3 + -1x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
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
Solution
x = {-3, 1}