6+3(k+4)=5k(k-9)

Solution for 6+3(k+4)=5k(k-9) equation:

Simplifying
6 + 3(k + 4) = 5k(k + -9)

Reorder the terms:
6 + 3(4 + k) = 5k(k + -9)
6 + (4 * 3 + k * 3) = 5k(k + -9)
6 + (12 + 3k) = 5k(k + -9)

Combine like terms: 6 + 12 = 18
18 + 3k = 5k(k + -9)

Reorder the terms:
18 + 3k = 5k(-9 + k)
18 + 3k = (-9 * 5k + k * 5k)
18 + 3k = (-45k + 5k2)

Solving
18 + 3k = -45k + 5k2

Solving for variable 'k'.

Combine like terms: 3k + 45k = 48k
18 + 48k + -5k2 = -45k + 5k2 + 45k + -5k2

Reorder the terms:
18 + 48k + -5k2 = -45k + 45k + 5k2 + -5k2

Combine like terms: -45k + 45k = 0
18 + 48k + -5k2 = 0 + 5k2 + -5k2
18 + 48k + -5k2 = 5k2 + -5k2

Combine like terms: 5k2 + -5k2 = 0
18 + 48k + -5k2 = 0

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

Divide each side by '-5'.
-3.6 + -9.6k + k2 = 0

Move the constant term to the right:

Add '3.6' to each side of the equation.
-3.6 + -9.6k + 3.6 + k2 = 0 + 3.6

Reorder the terms:
-3.6 + 3.6 + -9.6k + k2 = 0 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + -9.6k + k2 = 0 + 3.6
-9.6k + k2 = 0 + 3.6

Combine like terms: 0 + 3.6 = 3.6
-9.6k + k2 = 3.6

The k term is -9.6k.  Take half its coefficient (-4.8).
Square it (23.04) and add it to both sides.

Add '23.04' to each side of the equation.
-9.6k + 23.04 + k2 = 3.6 + 23.04

Reorder the terms:
23.04 + -9.6k + k2 = 3.6 + 23.04

Combine like terms: 3.6 + 23.04 = 26.64
23.04 + -9.6k + k2 = 26.64

Factor a perfect square on the left side:
(k + -4.8)(k + -4.8) = 26.64

Calculate the square root of the right side: 5.16139516

Break this problem into two subproblems by setting 
(k + -4.8) equal to 5.16139516 and -5.16139516.

Subproblem 1
k + -4.8 = 5.16139516

Simplifying
k + -4.8 = 5.16139516

Reorder the terms:
-4.8 + k = 5.16139516

Solving
-4.8 + k = 5.16139516

Solving for variable 'k'.

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

Add '4.8' to each side of the equation.
-4.8 + 4.8 + k = 5.16139516 + 4.8

Combine like terms: -4.8 + 4.8 = 0.0
0.0 + k = 5.16139516 + 4.8
k = 5.16139516 + 4.8

Combine like terms: 5.16139516 + 4.8 = 9.96139516
k = 9.96139516

Simplifying
k = 9.96139516

Subproblem 2
k + -4.8 = -5.16139516

Simplifying
k + -4.8 = -5.16139516

Reorder the terms:
-4.8 + k = -5.16139516

Solving
-4.8 + k = -5.16139516

Solving for variable 'k'.

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

Add '4.8' to each side of the equation.
-4.8 + 4.8 + k = -5.16139516 + 4.8

Combine like terms: -4.8 + 4.8 = 0.0
0.0 + k = -5.16139516 + 4.8
k = -5.16139516 + 4.8

Combine like terms: -5.16139516 + 4.8 = -0.36139516
k = -0.36139516

Simplifying
k = -0.36139516

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {9.96139516, -0.36139516}