(k+3)(k-6)=0

Solution for (k+3)(k-6)=0 equation:

Simplifying
(k + 3)(k + -6) = 0

Reorder the terms:
(3 + k)(k + -6) = 0

Reorder the terms:
(3 + k)(-6 + k) = 0

Multiply (3 + k) * (-6 + k)
(3(-6 + k) + k(-6 + k)) = 0
((-6 * 3 + k * 3) + k(-6 + k)) = 0
((-18 + 3k) + k(-6 + k)) = 0
(-18 + 3k + (-6 * k + k * k)) = 0
(-18 + 3k + (-6k + k2)) = 0

Combine like terms: 3k + -6k = -3k
(-18 + -3k + k2) = 0

Solving
-18 + -3k + k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-3 + -1k)(6 + -1k) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1k)' equal to zero and attempt to solve:

Simplifying
6 + -1k = 0

Solving
6 + -1k = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1k = 0 + -6

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

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

Divide each side by '-1'.
k = 6

Simplifying
k = 6
Solution
k = {-3, 6}