(k+5)(k-2)=0

Solution for (k+5)(k-2)=0 equation:

Simplifying
(k + 5)(k + -2) = 0

Reorder the terms:
(5 + k)(k + -2) = 0

Reorder the terms:
(5 + k)(-2 + k) = 0

Multiply (5 + k) * (-2 + k)
(5(-2 + k) + k(-2 + k)) = 0
((-2 * 5 + k * 5) + k(-2 + k)) = 0
((-10 + 5k) + k(-2 + k)) = 0
(-10 + 5k + (-2 * k + k * k)) = 0
(-10 + 5k + (-2k + k2)) = 0

Combine like terms: 5k + -2k = 3k
(-10 + 3k + k2) = 0

Solving
-10 + 3k + k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-5 + -1k)(2 + -1k) = 0

Subproblem 1
Set the factor '(-5 + -1k)' equal to zero and attempt to solve:

Simplifying
-5 + -1k = 0

Solving
-5 + -1k = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1k = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1k = 0 + 5
-1k = 0 + 5

Combine like terms: 0 + 5 = 5
-1k = 5

Divide each side by '-1'.
k = -5

Simplifying
k = -5
Subproblem 2
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
Solution
k = {-5, 2}