(3k+5)(k-9)=15(k+3)

Solution for (3k+5)(k-9)=15(k+3) equation:

Simplifying
(3k + 5)(k + -9) = 15(k + 3)

Reorder the terms:
(5 + 3k)(k + -9) = 15(k + 3)

Reorder the terms:
(5 + 3k)(-9 + k) = 15(k + 3)

Multiply (5 + 3k) * (-9 + k)
(5(-9 + k) + 3k * (-9 + k)) = 15(k + 3)
((-9 * 5 + k * 5) + 3k * (-9 + k)) = 15(k + 3)
((-45 + 5k) + 3k * (-9 + k)) = 15(k + 3)
(-45 + 5k + (-9 * 3k + k * 3k)) = 15(k + 3)
(-45 + 5k + (-27k + 3k2)) = 15(k + 3)

Combine like terms: 5k + -27k = -22k
(-45 + -22k + 3k2) = 15(k + 3)

Reorder the terms:
-45 + -22k + 3k2 = 15(3 + k)
-45 + -22k + 3k2 = (3 * 15 + k * 15)
-45 + -22k + 3k2 = (45 + 15k)

Solving
-45 + -22k + 3k2 = 45 + 15k

Solving for variable 'k'.

Reorder the terms:
-45 + -45 + -22k + -15k + 3k2 = 45 + 15k + -45 + -15k

Combine like terms: -45 + -45 = -90
-90 + -22k + -15k + 3k2 = 45 + 15k + -45 + -15k

Combine like terms: -22k + -15k = -37k
-90 + -37k + 3k2 = 45 + 15k + -45 + -15k

Reorder the terms:
-90 + -37k + 3k2 = 45 + -45 + 15k + -15k

Combine like terms: 45 + -45 = 0
-90 + -37k + 3k2 = 0 + 15k + -15k
-90 + -37k + 3k2 = 15k + -15k

Combine like terms: 15k + -15k = 0
-90 + -37k + 3k2 = 0

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

Divide each side by '3'.
-30 + -12.33333333k + k2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -12.33333333k + 30 + k2 = 0 + 30

Reorder the terms:
-30 + 30 + -12.33333333k + k2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -12.33333333k + k2 = 0 + 30
-12.33333333k + k2 = 0 + 30

Combine like terms: 0 + 30 = 30
-12.33333333k + k2 = 30

The k term is -12.33333333k.  Take half its coefficient (-6.166666665).
Square it (38.02777776) and add it to both sides.

Add '38.02777776' to each side of the equation.
-12.33333333k + 38.02777776 + k2 = 30 + 38.02777776

Reorder the terms:
38.02777776 + -12.33333333k + k2 = 30 + 38.02777776

Combine like terms: 30 + 38.02777776 = 68.02777776
38.02777776 + -12.33333333k + k2 = 68.02777776

Factor a perfect square on the left side:
(k + -6.166666665)(k + -6.166666665) = 68.02777776

Calculate the square root of the right side: 8.247895353

Break this problem into two subproblems by setting 
(k + -6.166666665) equal to 8.247895353 and -8.247895353.

Subproblem 1
k + -6.166666665 = 8.247895353

Simplifying
k + -6.166666665 = 8.247895353

Reorder the terms:
-6.166666665 + k = 8.247895353

Solving
-6.166666665 + k = 8.247895353

Solving for variable 'k'.

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

Add '6.166666665' to each side of the equation.
-6.166666665 + 6.166666665 + k = 8.247895353 + 6.166666665

Combine like terms: -6.166666665 + 6.166666665 = 0.000000000
0.000000000 + k = 8.247895353 + 6.166666665
k = 8.247895353 + 6.166666665

Combine like terms: 8.247895353 + 6.166666665 = 14.414562018
k = 14.414562018

Simplifying
k = 14.414562018

Subproblem 2
k + -6.166666665 = -8.247895353

Simplifying
k + -6.166666665 = -8.247895353

Reorder the terms:
-6.166666665 + k = -8.247895353

Solving
-6.166666665 + k = -8.247895353

Solving for variable 'k'.

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

Add '6.166666665' to each side of the equation.
-6.166666665 + 6.166666665 + k = -8.247895353 + 6.166666665

Combine like terms: -6.166666665 + 6.166666665 = 0.000000000
0.000000000 + k = -8.247895353 + 6.166666665
k = -8.247895353 + 6.166666665

Combine like terms: -8.247895353 + 6.166666665 = -2.081228688
k = -2.081228688

Simplifying
k = -2.081228688

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {14.414562018, -2.081228688}