(k+2)(k+1)=2

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

Simplifying
(k + 2)(k + 1) = 2

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

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

Multiply (2 + k) * (1 + k)
(2(1 + k) + k(1 + k)) = 2
((1 * 2 + k * 2) + k(1 + k)) = 2
((2 + 2k) + k(1 + k)) = 2
(2 + 2k + (1 * k + k * k)) = 2
(2 + 2k + (1k + k2)) = 2

Combine like terms: 2k + 1k = 3k
(2 + 3k + k2) = 2

Add '-2' to each side of the equation.
2 + 3k + -2 + k2 = 2 + -2

Reorder the terms:
2 + -2 + 3k + k2 = 2 + -2

Combine like terms: 2 + -2 = 0
0 + 3k + k2 = 2 + -2
3k + k2 = 2 + -2

Combine like terms: 2 + -2 = 0
3k + k2 = 0

Solving
3k + k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), 'k'.
k(3 + k) = 0

Subproblem 1
Set the factor 'k' equal to zero and attempt to solve:

Simplifying
k = 0

Solving
k = 0

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

Simplifying
k = 0
Subproblem 2
Set the factor '(3 + k)' equal to zero and attempt to solve:

Simplifying
3 + k = 0

Solving
3 + k = 0

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

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

Combine like terms: 3 + -3 = 0
0 + k = 0 + -3
k = 0 + -3

Combine like terms: 0 + -3 = -3
k = -3

Simplifying
k = -3
Solution
k = {0, -3}