K^2+4K-105=-9

Solution for K^2+4K-105=-9 equation:

Simplifying
K2 + 4K + -105 = -9

Reorder the terms:
-105 + 4K + K2 = -9

Solving
-105 + 4K + K2 = -9

Solving for variable 'K'.

Reorder the terms:
-105 + 9 + 4K + K2 = -9 + 9

Combine like terms: -105 + 9 = -96
-96 + 4K + K2 = -9 + 9

Combine like terms: -9 + 9 = 0
-96 + 4K + K2 = 0

Factor a trinomial.
(-12 + -1K)(8 + -1K) = 0

Subproblem 1
Set the factor '(-12 + -1K)' equal to zero and attempt to solve:

Simplifying
-12 + -1K = 0

Solving
-12 + -1K = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1K = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1K = 0 + 12
-1K = 0 + 12

Combine like terms: 0 + 12 = 12
-1K = 12

Divide each side by '-1'.
K = -12

Simplifying
K = -12
Subproblem 2
Set the factor '(8 + -1K)' equal to zero and attempt to solve:

Simplifying
8 + -1K = 0

Solving
8 + -1K = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1K = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1K = 0 + -8
-1K = 0 + -8

Combine like terms: 0 + -8 = -8
-1K = -8

Divide each side by '-1'.
K = 8

Simplifying
K = 8
Solution
K = {-12, 8}