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

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


Simplifying
(3k + 5)(9 + -1k) = 15(k + 3)

Reorder the terms:
(5 + 3k)(9 + -1k) = 15(k + 3)

Multiply (5 + 3k) * (9 + -1k)
(5(9 + -1k) + 3k * (9 + -1k)) = 15(k + 3)
((9 * 5 + -1k * 5) + 3k * (9 + -1k)) = 15(k + 3)
((45 + -5k) + 3k * (9 + -1k)) = 15(k + 3)
(45 + -5k + (9 * 3k + -1k * 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)

Add '-45' to each side of the equation.
45 + 22k + -45 + -3k2 = 45 + -45 + 15k

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

Combine like terms: 45 + -45 = 0
0 + 22k + -3k2 = 45 + -45 + 15k
22k + -3k2 = 45 + -45 + 15k

Combine like terms: 45 + -45 = 0
22k + -3k2 = 0 + 15k
22k + -3k2 = 15k

Solving
22k + -3k2 = 15k

Solving for variable 'k'.

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

Combine like terms: 22k + -15k = 7k
7k + -3k2 = 15k + -15k

Combine like terms: 15k + -15k = 0
7k + -3k2 = 0

Factor out the Greatest Common Factor (GCF), 'k'.
k(7 + -3k) = 0


Subproblem 1
Set the factor 'k' equal to zero and attempt to solve:

Simplifying
k = 0

Solving
k = 0

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

Simplifying
k = 0

Subproblem 2
Set the factor '(7 + -3k)' equal to zero and attempt to solve:

Simplifying
7 + -3k = 0

Solving
7 + -3k = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3k = 0 + -7
-3k = 0 + -7

Combine like terms: 0 + -7 = -7
-3k = -7

Divide each side by '-3'.
k = 2.333333333

Simplifying
k = 2.333333333
Solution
k = {0, 2.333333333}

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