3(2k-4)=-3k(k+2)+21

Solution for 3(2k-4)=-3k(k+2)+21 equation:

Simplifying
3(2k + -4) = -3k(k + 2) + 21

Reorder the terms:
3(-4 + 2k) = -3k(k + 2) + 21
(-4 * 3 + 2k * 3) = -3k(k + 2) + 21
(-12 + 6k) = -3k(k + 2) + 21

Reorder the terms:
-12 + 6k = -3k(2 + k) + 21
-12 + 6k = (2 * -3k + k * -3k) + 21
-12 + 6k = (-6k + -3k2) + 21

Reorder the terms:
-12 + 6k = 21 + -6k + -3k2

Solving
-12 + 6k = 21 + -6k + -3k2

Solving for variable 'k'.

Reorder the terms:
-12 + -21 + 6k + 6k + 3k2 = 21 + -6k + -3k2 + -21 + 6k + 3k2

Combine like terms: -12 + -21 = -33
-33 + 6k + 6k + 3k2 = 21 + -6k + -3k2 + -21 + 6k + 3k2

Combine like terms: 6k + 6k = 12k
-33 + 12k + 3k2 = 21 + -6k + -3k2 + -21 + 6k + 3k2

Reorder the terms:
-33 + 12k + 3k2 = 21 + -21 + -6k + 6k + -3k2 + 3k2

Combine like terms: 21 + -21 = 0
-33 + 12k + 3k2 = 0 + -6k + 6k + -3k2 + 3k2
-33 + 12k + 3k2 = -6k + 6k + -3k2 + 3k2

Combine like terms: -6k + 6k = 0
-33 + 12k + 3k2 = 0 + -3k2 + 3k2
-33 + 12k + 3k2 = -3k2 + 3k2

Combine like terms: -3k2 + 3k2 = 0
-33 + 12k + 3k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-11 + 4k + k2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-11 + 4k + k2)' equal to zero and attempt to solve:

Simplifying
-11 + 4k + k2 = 0

Solving
-11 + 4k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 4k + 11 + k2 = 0 + 11

Reorder the terms:
-11 + 11 + 4k + k2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 4k + k2 = 0 + 11
4k + k2 = 0 + 11

Combine like terms: 0 + 11 = 11
4k + k2 = 11

The k term is 4k.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4k + 4 + k2 = 11 + 4

Reorder the terms:
4 + 4k + k2 = 11 + 4

Combine like terms: 11 + 4 = 15
4 + 4k + k2 = 15

Factor a perfect square on the left side:
(k + 2)(k + 2) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(k + 2) equal to 3.872983346 and -3.872983346.

Subproblem 1
k + 2 = 3.872983346

Simplifying
k + 2 = 3.872983346

Reorder the terms:
2 + k = 3.872983346

Solving
2 + k = 3.872983346

Solving for variable 'k'.

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

Add '-2' to each side of the equation.
2 + -2 + k = 3.872983346 + -2

Combine like terms: 2 + -2 = 0
0 + k = 3.872983346 + -2
k = 3.872983346 + -2

Combine like terms: 3.872983346 + -2 = 1.872983346
k = 1.872983346

Simplifying
k = 1.872983346

Subproblem 2
k + 2 = -3.872983346

Simplifying
k + 2 = -3.872983346

Reorder the terms:
2 + k = -3.872983346

Solving
2 + k = -3.872983346

Solving for variable 'k'.

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

Add '-2' to each side of the equation.
2 + -2 + k = -3.872983346 + -2

Combine like terms: 2 + -2 = 0
0 + k = -3.872983346 + -2
k = -3.872983346 + -2

Combine like terms: -3.872983346 + -2 = -5.872983346
k = -5.872983346

Simplifying
k = -5.872983346

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.872983346, -5.872983346}
Solution
k = {1.872983346, -5.872983346}