5k(k-2)=10(3k+9)

Solution for 5k(k-2)=10(3k+9) equation:

Simplifying
5k(k + -2) = 10(3k + 9)

Reorder the terms:
5k(-2 + k) = 10(3k + 9)
(-2 * 5k + k * 5k) = 10(3k + 9)
(-10k + 5k2) = 10(3k + 9)

Reorder the terms:
-10k + 5k2 = 10(9 + 3k)
-10k + 5k2 = (9 * 10 + 3k * 10)
-10k + 5k2 = (90 + 30k)

Solving
-10k + 5k2 = 90 + 30k

Solving for variable 'k'.

Reorder the terms:
-90 + -10k + -30k + 5k2 = 90 + 30k + -90 + -30k

Combine like terms: -10k + -30k = -40k
-90 + -40k + 5k2 = 90 + 30k + -90 + -30k

Reorder the terms:
-90 + -40k + 5k2 = 90 + -90 + 30k + -30k

Combine like terms: 90 + -90 = 0
-90 + -40k + 5k2 = 0 + 30k + -30k
-90 + -40k + 5k2 = 30k + -30k

Combine like terms: 30k + -30k = 0
-90 + -40k + 5k2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-18 + -8k + k2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-18 + -8k + k2)' equal to zero and attempt to solve:

Simplifying
-18 + -8k + k2 = 0

Solving
-18 + -8k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -8k + 18 + k2 = 0 + 18

Reorder the terms:
-18 + 18 + -8k + k2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -8k + k2 = 0 + 18
-8k + k2 = 0 + 18

Combine like terms: 0 + 18 = 18
-8k + k2 = 18

The k term is -8k.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8k + 16 + k2 = 18 + 16

Reorder the terms:
16 + -8k + k2 = 18 + 16

Combine like terms: 18 + 16 = 34
16 + -8k + k2 = 34

Factor a perfect square on the left side:
(k + -4)(k + -4) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(k + -4) equal to 5.830951895 and -5.830951895.

Subproblem 1
k + -4 = 5.830951895

Simplifying
k + -4 = 5.830951895

Reorder the terms:
-4 + k = 5.830951895

Solving
-4 + k = 5.830951895

Solving for variable 'k'.

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

Add '4' to each side of the equation.
-4 + 4 + k = 5.830951895 + 4

Combine like terms: -4 + 4 = 0
0 + k = 5.830951895 + 4
k = 5.830951895 + 4

Combine like terms: 5.830951895 + 4 = 9.830951895
k = 9.830951895

Simplifying
k = 9.830951895

Subproblem 2
k + -4 = -5.830951895

Simplifying
k + -4 = -5.830951895

Reorder the terms:
-4 + k = -5.830951895

Solving
-4 + k = -5.830951895

Solving for variable 'k'.

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

Add '4' to each side of the equation.
-4 + 4 + k = -5.830951895 + 4

Combine like terms: -4 + 4 = 0
0 + k = -5.830951895 + 4
k = -5.830951895 + 4

Combine like terms: -5.830951895 + 4 = -1.830951895
k = -1.830951895

Simplifying
k = -1.830951895

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {9.830951895, -1.830951895}
Solution
k = {9.830951895, -1.830951895}