4=4k(k+3)

Solution for 4=4k(k+3) equation:

Simplifying
4 = 4k(k + 3)

Reorder the terms:
4 = 4k(3 + k)
4 = (3 * 4k + k * 4k)
4 = (12k + 4k2)

Solving
4 = 12k + 4k2

Solving for variable 'k'.

Reorder the terms:
4 + -12k + -4k2 = 12k + -12k + 4k2 + -4k2

Combine like terms: 12k + -12k = 0
4 + -12k + -4k2 = 0 + 4k2 + -4k2
4 + -12k + -4k2 = 4k2 + -4k2

Combine like terms: 4k2 + -4k2 = 0
4 + -12k + -4k2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + -3k + -1k2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + -3k + -1k2)' equal to zero and attempt to solve:

Simplifying
1 + -3k + -1k2 = 0

Solving
1 + -3k + -1k2 = 0

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

Divide each side by '-1'.
-1 + 3k + k2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 3k + 1 + k2 = 0 + 1

Reorder the terms:
-1 + 1 + 3k + k2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3k + k2 = 0 + 1
3k + k2 = 0 + 1

Combine like terms: 0 + 1 = 1
3k + k2 = 1

The k term is 3k.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3k + 2.25 + k2 = 1 + 2.25

Reorder the terms:
2.25 + 3k + k2 = 1 + 2.25

Combine like terms: 1 + 2.25 = 3.25
2.25 + 3k + k2 = 3.25

Factor a perfect square on the left side:
(k + 1.5)(k + 1.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(k + 1.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
k + 1.5 = 1.802775638

Simplifying
k + 1.5 = 1.802775638

Reorder the terms:
1.5 + k = 1.802775638

Solving
1.5 + k = 1.802775638

Solving for variable 'k'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + k = 1.802775638 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + k = 1.802775638 + -1.5
k = 1.802775638 + -1.5

Combine like terms: 1.802775638 + -1.5 = 0.302775638
k = 0.302775638

Simplifying
k = 0.302775638

Subproblem 2
k + 1.5 = -1.802775638

Simplifying
k + 1.5 = -1.802775638

Reorder the terms:
1.5 + k = -1.802775638

Solving
1.5 + k = -1.802775638

Solving for variable 'k'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + k = -1.802775638 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + k = -1.802775638 + -1.5
k = -1.802775638 + -1.5

Combine like terms: -1.802775638 + -1.5 = -3.302775638
k = -3.302775638

Simplifying
k = -3.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.302775638, -3.302775638}
Solution
k = {0.302775638, -3.302775638}