K(K+3)=5K+3

Solution for K(K+3)=5K+3 equation:

Simplifying
K(K + 3) = 5K + 3

Reorder the terms:
K(3 + K) = 5K + 3
(3 * K + K * K) = 5K + 3
(3K + K2) = 5K + 3

Reorder the terms:
3K + K2 = 3 + 5K

Solving
3K + K2 = 3 + 5K

Solving for variable 'K'.

Reorder the terms:
-3 + 3K + -5K + K2 = 3 + 5K + -3 + -5K

Combine like terms: 3K + -5K = -2K
-3 + -2K + K2 = 3 + 5K + -3 + -5K

Reorder the terms:
-3 + -2K + K2 = 3 + -3 + 5K + -5K

Combine like terms: 3 + -3 = 0
-3 + -2K + K2 = 0 + 5K + -5K
-3 + -2K + K2 = 5K + -5K

Combine like terms: 5K + -5K = 0
-3 + -2K + K2 = 0

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

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

Simplifying
-1 + -1K = 0

Solving
-1 + -1K = 0

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

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

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

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

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

Simplifying
K = -1
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 = {-1, 3}