(K-6)(K+3)=

Solution for (K-6)(K+3)= equation:

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

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

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

Multiply (-6 + K) * (3 + K)
(-6(3 + K) + K(3 + K)) = 0
((3 * -6 + K * -6) + K(3 + K)) = 0
((-18 + -6K) + K(3 + K)) = 0
(-18 + -6K + (3 * K + K * K)) = 0
(-18 + -6K + (3K + K2)) = 0

Combine like terms: -6K + 3K = -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}