(k+1)(k-2)=4

Solution for (k+1)(k-2)=4 equation:

Simplifying
(k + 1)(k + -2) = 4

Reorder the terms:
(1 + k)(k + -2) = 4

Reorder the terms:
(1 + k)(-2 + k) = 4

Multiply (1 + k) * (-2 + k)
(1(-2 + k) + k(-2 + k)) = 4
((-2 * 1 + k * 1) + k(-2 + k)) = 4
((-2 + 1k) + k(-2 + k)) = 4
(-2 + 1k + (-2 * k + k * k)) = 4
(-2 + 1k + (-2k + k2)) = 4

Combine like terms: 1k + -2k = -1k
(-2 + -1k + k2) = 4

Solving
-2 + -1k + k2 = 4

Solving for variable 'k'.

Reorder the terms:
-2 + -4 + -1k + k2 = 4 + -4

Combine like terms: -2 + -4 = -6
-6 + -1k + k2 = 4 + -4

Combine like terms: 4 + -4 = 0
-6 + -1k + k2 = 0

Factor a trinomial.
(-2 + -1k)(3 + -1k) = 0

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

Simplifying
-2 + -1k = 0

Solving
-2 + -1k = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1k = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1k = 0 + 2
-1k = 0 + 2

Combine like terms: 0 + 2 = 2
-1k = 2

Divide each side by '-1'.
k = -2

Simplifying
k = -2
Subproblem 2
Set the factor '(3 + -1k)' equal to zero and attempt to solve:

Simplifying
3 + -1k = 0

Solving
3 + -1k = 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 + -1k = 0 + -3

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

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

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

Simplifying
k = 3
Solution
k = {-2, 3}