4(k-3)+7=2k(k+8)

Solution for 4(k-3)+7=2k(k+8) equation:

Simplifying
4(k + -3) + 7 = 2k(k + 8)

Reorder the terms:
4(-3 + k) + 7 = 2k(k + 8)
(-3 * 4 + k * 4) + 7 = 2k(k + 8)
(-12 + 4k) + 7 = 2k(k + 8)

Reorder the terms:
-12 + 7 + 4k = 2k(k + 8)

Combine like terms: -12 + 7 = -5
-5 + 4k = 2k(k + 8)

Reorder the terms:
-5 + 4k = 2k(8 + k)
-5 + 4k = (8 * 2k + k * 2k)
-5 + 4k = (16k + 2k2)

Solving
-5 + 4k = 16k + 2k2

Solving for variable 'k'.

Combine like terms: 4k + -16k = -12k
-5 + -12k + -2k2 = 16k + 2k2 + -16k + -2k2

Reorder the terms:
-5 + -12k + -2k2 = 16k + -16k + 2k2 + -2k2

Combine like terms: 16k + -16k = 0
-5 + -12k + -2k2 = 0 + 2k2 + -2k2
-5 + -12k + -2k2 = 2k2 + -2k2

Combine like terms: 2k2 + -2k2 = 0
-5 + -12k + -2k2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 12k + 2k2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + 12k + 2k2)' equal to zero and attempt to solve:

Simplifying
5 + 12k + 2k2 = 0

Solving
5 + 12k + 2k2 = 0

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

Divide each side by '2'.
2.5 + 6k + k2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 6k + -2.5 + k2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 6k + k2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 6k + k2 = 0 + -2.5
6k + k2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
6k + k2 = -2.5

The k term is 6k.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6k + 9 + k2 = -2.5 + 9

Reorder the terms:
9 + 6k + k2 = -2.5 + 9

Combine like terms: -2.5 + 9 = 6.5
9 + 6k + k2 = 6.5

Factor a perfect square on the left side:
(k + 3)(k + 3) = 6.5

Calculate the square root of the right side: 2.549509757

Break this problem into two subproblems by setting 
(k + 3) equal to 2.549509757 and -2.549509757.

Subproblem 1
k + 3 = 2.549509757

Simplifying
k + 3 = 2.549509757

Reorder the terms:
3 + k = 2.549509757

Solving
3 + k = 2.549509757

Solving for variable 'k'.

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

Add '-3' to each side of the equation.
3 + -3 + k = 2.549509757 + -3

Combine like terms: 3 + -3 = 0
0 + k = 2.549509757 + -3
k = 2.549509757 + -3

Combine like terms: 2.549509757 + -3 = -0.450490243
k = -0.450490243

Simplifying
k = -0.450490243

Subproblem 2
k + 3 = -2.549509757

Simplifying
k + 3 = -2.549509757

Reorder the terms:
3 + k = -2.549509757

Solving
3 + k = -2.549509757

Solving for variable 'k'.

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

Add '-3' to each side of the equation.
3 + -3 + k = -2.549509757 + -3

Combine like terms: 3 + -3 = 0
0 + k = -2.549509757 + -3
k = -2.549509757 + -3

Combine like terms: -2.549509757 + -3 = -5.549509757
k = -5.549509757

Simplifying
k = -5.549509757

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {-0.450490243, -5.549509757}
Solution
k = {-0.450490243, -5.549509757}