5k(3+k)=(3k+3)

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

Simplifying
5k(3 + k) = (3k + 3)
(3 * 5k + k * 5k) = (3k + 3)
(15k + 5k2) = (3k + 3)

Reorder the terms:
15k + 5k2 = (3 + 3k)

Remove parenthesis around (3 + 3k)
15k + 5k2 = 3 + 3k

Solving
15k + 5k2 = 3 + 3k

Solving for variable 'k'.

Reorder the terms:
-3 + 15k + -3k + 5k2 = 3 + 3k + -3 + -3k

Combine like terms: 15k + -3k = 12k
-3 + 12k + 5k2 = 3 + 3k + -3 + -3k

Reorder the terms:
-3 + 12k + 5k2 = 3 + -3 + 3k + -3k

Combine like terms: 3 + -3 = 0
-3 + 12k + 5k2 = 0 + 3k + -3k
-3 + 12k + 5k2 = 3k + -3k

Combine like terms: 3k + -3k = 0
-3 + 12k + 5k2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-0.6 + 2.4k + k2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 2.4k + 0.6 + k2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 2.4k + k2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 2.4k + k2 = 0 + 0.6
2.4k + k2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
2.4k + k2 = 0.6

The k term is 2.4k.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4k + 1.44 + k2 = 0.6 + 1.44

Reorder the terms:
1.44 + 2.4k + k2 = 0.6 + 1.44

Combine like terms: 0.6 + 1.44 = 2.04
1.44 + 2.4k + k2 = 2.04

Factor a perfect square on the left side:
(k + 1.2)(k + 1.2) = 2.04

Calculate the square root of the right side: 1.428285686

Break this problem into two subproblems by setting 
(k + 1.2) equal to 1.428285686 and -1.428285686.

Subproblem 1
k + 1.2 = 1.428285686

Simplifying
k + 1.2 = 1.428285686

Reorder the terms:
1.2 + k = 1.428285686

Solving
1.2 + k = 1.428285686

Solving for variable 'k'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + k = 1.428285686 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + k = 1.428285686 + -1.2
k = 1.428285686 + -1.2

Combine like terms: 1.428285686 + -1.2 = 0.228285686
k = 0.228285686

Simplifying
k = 0.228285686

Subproblem 2
k + 1.2 = -1.428285686

Simplifying
k + 1.2 = -1.428285686

Reorder the terms:
1.2 + k = -1.428285686

Solving
1.2 + k = -1.428285686

Solving for variable 'k'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + k = -1.428285686 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + k = -1.428285686 + -1.2
k = -1.428285686 + -1.2

Combine like terms: -1.428285686 + -1.2 = -2.628285686
k = -2.628285686

Simplifying
k = -2.628285686

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.228285686, -2.628285686}