3k(k+7)=(k-2)(k-2)

Solution for 3k(k+7)=(k-2)(k-2) equation:

Simplifying
3k(k + 7) = (k + -2)(k + -2)

Reorder the terms:
3k(7 + k) = (k + -2)(k + -2)
(7 * 3k + k * 3k) = (k + -2)(k + -2)
(21k + 3k2) = (k + -2)(k + -2)

Reorder the terms:
21k + 3k2 = (-2 + k)(k + -2)

Reorder the terms:
21k + 3k2 = (-2 + k)(-2 + k)

Multiply (-2 + k) * (-2 + k)
21k + 3k2 = (-2(-2 + k) + k(-2 + k))
21k + 3k2 = ((-2 * -2 + k * -2) + k(-2 + k))
21k + 3k2 = ((4 + -2k) + k(-2 + k))
21k + 3k2 = (4 + -2k + (-2 * k + k * k))
21k + 3k2 = (4 + -2k + (-2k + k2))

Combine like terms: -2k + -2k = -4k
21k + 3k2 = (4 + -4k + k2)

Solving
21k + 3k2 = 4 + -4k + k2

Solving for variable 'k'.

Reorder the terms:
-4 + 21k + 4k + 3k2 + -1k2 = 4 + -4k + k2 + -4 + 4k + -1k2

Combine like terms: 21k + 4k = 25k
-4 + 25k + 3k2 + -1k2 = 4 + -4k + k2 + -4 + 4k + -1k2

Combine like terms: 3k2 + -1k2 = 2k2
-4 + 25k + 2k2 = 4 + -4k + k2 + -4 + 4k + -1k2

Reorder the terms:
-4 + 25k + 2k2 = 4 + -4 + -4k + 4k + k2 + -1k2

Combine like terms: 4 + -4 = 0
-4 + 25k + 2k2 = 0 + -4k + 4k + k2 + -1k2
-4 + 25k + 2k2 = -4k + 4k + k2 + -1k2

Combine like terms: -4k + 4k = 0
-4 + 25k + 2k2 = 0 + k2 + -1k2
-4 + 25k + 2k2 = k2 + -1k2

Combine like terms: k2 + -1k2 = 0
-4 + 25k + 2k2 = 0

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

Divide each side by '2'.
-2 + 12.5k + k2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 12.5k + 2 + k2 = 0 + 2

Reorder the terms:
-2 + 2 + 12.5k + k2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 12.5k + k2 = 0 + 2
12.5k + k2 = 0 + 2

Combine like terms: 0 + 2 = 2
12.5k + k2 = 2

The k term is 12.5k.  Take half its coefficient (6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
12.5k + 39.0625 + k2 = 2 + 39.0625

Reorder the terms:
39.0625 + 12.5k + k2 = 2 + 39.0625

Combine like terms: 2 + 39.0625 = 41.0625
39.0625 + 12.5k + k2 = 41.0625

Factor a perfect square on the left side:
(k + 6.25)(k + 6.25) = 41.0625

Calculate the square root of the right side: 6.408002809

Break this problem into two subproblems by setting 
(k + 6.25) equal to 6.408002809 and -6.408002809.

Subproblem 1
k + 6.25 = 6.408002809

Simplifying
k + 6.25 = 6.408002809

Reorder the terms:
6.25 + k = 6.408002809

Solving
6.25 + k = 6.408002809

Solving for variable 'k'.

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

Add '-6.25' to each side of the equation.
6.25 + -6.25 + k = 6.408002809 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + k = 6.408002809 + -6.25
k = 6.408002809 + -6.25

Combine like terms: 6.408002809 + -6.25 = 0.158002809
k = 0.158002809

Simplifying
k = 0.158002809

Subproblem 2
k + 6.25 = -6.408002809

Simplifying
k + 6.25 = -6.408002809

Reorder the terms:
6.25 + k = -6.408002809

Solving
6.25 + k = -6.408002809

Solving for variable 'k'.

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

Add '-6.25' to each side of the equation.
6.25 + -6.25 + k = -6.408002809 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + k = -6.408002809 + -6.25
k = -6.408002809 + -6.25

Combine like terms: -6.408002809 + -6.25 = -12.658002809
k = -12.658002809

Simplifying
k = -12.658002809

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.158002809, -12.658002809}