k(k-7)+10=2k(k+6)

Solution for k(k-7)+10=2k(k+6) equation:

Simplifying
k(k + -7) + 10 = 2k(k + 6)

Reorder the terms:
k(-7 + k) + 10 = 2k(k + 6)
(-7 * k + k * k) + 10 = 2k(k + 6)
(-7k + k2) + 10 = 2k(k + 6)

Reorder the terms:
10 + -7k + k2 = 2k(k + 6)

Reorder the terms:
10 + -7k + k2 = 2k(6 + k)
10 + -7k + k2 = (6 * 2k + k * 2k)
10 + -7k + k2 = (12k + 2k2)

Solving
10 + -7k + k2 = 12k + 2k2

Solving for variable 'k'.

Reorder the terms:
10 + -7k + -12k + k2 + -2k2 = 12k + 2k2 + -12k + -2k2

Combine like terms: -7k + -12k = -19k
10 + -19k + k2 + -2k2 = 12k + 2k2 + -12k + -2k2

Combine like terms: k2 + -2k2 = -1k2
10 + -19k + -1k2 = 12k + 2k2 + -12k + -2k2

Reorder the terms:
10 + -19k + -1k2 = 12k + -12k + 2k2 + -2k2

Combine like terms: 12k + -12k = 0
10 + -19k + -1k2 = 0 + 2k2 + -2k2
10 + -19k + -1k2 = 2k2 + -2k2

Combine like terms: 2k2 + -2k2 = 0
10 + -19k + -1k2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-10 + 19k + k2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 19k + 10 + k2 = 0 + 10

Reorder the terms:
-10 + 10 + 19k + k2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 19k + k2 = 0 + 10
19k + k2 = 0 + 10

Combine like terms: 0 + 10 = 10
19k + k2 = 10

The k term is 19k.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19k + 90.25 + k2 = 10 + 90.25

Reorder the terms:
90.25 + 19k + k2 = 10 + 90.25

Combine like terms: 10 + 90.25 = 100.25
90.25 + 19k + k2 = 100.25

Factor a perfect square on the left side:
(k + 9.5)(k + 9.5) = 100.25

Calculate the square root of the right side: 10.012492197

Break this problem into two subproblems by setting 
(k + 9.5) equal to 10.012492197 and -10.012492197.

Subproblem 1
k + 9.5 = 10.012492197

Simplifying
k + 9.5 = 10.012492197

Reorder the terms:
9.5 + k = 10.012492197

Solving
9.5 + k = 10.012492197

Solving for variable 'k'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + k = 10.012492197 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + k = 10.012492197 + -9.5
k = 10.012492197 + -9.5

Combine like terms: 10.012492197 + -9.5 = 0.512492197
k = 0.512492197

Simplifying
k = 0.512492197

Subproblem 2
k + 9.5 = -10.012492197

Simplifying
k + 9.5 = -10.012492197

Reorder the terms:
9.5 + k = -10.012492197

Solving
9.5 + k = -10.012492197

Solving for variable 'k'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + k = -10.012492197 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + k = -10.012492197 + -9.5
k = -10.012492197 + -9.5

Combine like terms: -10.012492197 + -9.5 = -19.512492197
k = -19.512492197

Simplifying
k = -19.512492197

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.512492197, -19.512492197}