3(6k+14)-12k(k-9)-3=

Solution for 3(6k+14)-12k(k-9)-3= equation:

Simplifying
3(6k + 14) + -12k(k + -9) + -3 = 0

Reorder the terms:
3(14 + 6k) + -12k(k + -9) + -3 = 0
(14 * 3 + 6k * 3) + -12k(k + -9) + -3 = 0
(42 + 18k) + -12k(k + -9) + -3 = 0

Reorder the terms:
42 + 18k + -12k(-9 + k) + -3 = 0
42 + 18k + (-9 * -12k + k * -12k) + -3 = 0
42 + 18k + (108k + -12k2) + -3 = 0

Reorder the terms:
42 + -3 + 18k + 108k + -12k2 = 0

Combine like terms: 42 + -3 = 39
39 + 18k + 108k + -12k2 = 0

Combine like terms: 18k + 108k = 126k
39 + 126k + -12k2 = 0

Solving
39 + 126k + -12k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3'.
3(13 + 42k + -4k2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(13 + 42k + -4k2)' equal to zero and attempt to solve:

Simplifying
13 + 42k + -4k2 = 0

Solving
13 + 42k + -4k2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-3.25 + -10.5k + k2 = 0

Move the constant term to the right:

Add '3.25' to each side of the equation.
-3.25 + -10.5k + 3.25 + k2 = 0 + 3.25

Reorder the terms:
-3.25 + 3.25 + -10.5k + k2 = 0 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + -10.5k + k2 = 0 + 3.25
-10.5k + k2 = 0 + 3.25

Combine like terms: 0 + 3.25 = 3.25
-10.5k + k2 = 3.25

The k term is -10.5k.  Take half its coefficient (-5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
-10.5k + 27.5625 + k2 = 3.25 + 27.5625

Reorder the terms:
27.5625 + -10.5k + k2 = 3.25 + 27.5625

Combine like terms: 3.25 + 27.5625 = 30.8125
27.5625 + -10.5k + k2 = 30.8125

Factor a perfect square on the left side:
(k + -5.25)(k + -5.25) = 30.8125

Calculate the square root of the right side: 5.550900828

Break this problem into two subproblems by setting 
(k + -5.25) equal to 5.550900828 and -5.550900828.

Subproblem 1
k + -5.25 = 5.550900828

Simplifying
k + -5.25 = 5.550900828

Reorder the terms:
-5.25 + k = 5.550900828

Solving
-5.25 + k = 5.550900828

Solving for variable 'k'.

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

Add '5.25' to each side of the equation.
-5.25 + 5.25 + k = 5.550900828 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + k = 5.550900828 + 5.25
k = 5.550900828 + 5.25

Combine like terms: 5.550900828 + 5.25 = 10.800900828
k = 10.800900828

Simplifying
k = 10.800900828

Subproblem 2
k + -5.25 = -5.550900828

Simplifying
k + -5.25 = -5.550900828

Reorder the terms:
-5.25 + k = -5.550900828

Solving
-5.25 + k = -5.550900828

Solving for variable 'k'.

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

Add '5.25' to each side of the equation.
-5.25 + 5.25 + k = -5.550900828 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + k = -5.550900828 + 5.25
k = -5.550900828 + 5.25

Combine like terms: -5.550900828 + 5.25 = -0.300900828
k = -0.300900828

Simplifying
k = -0.300900828

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {10.800900828, -0.300900828}
Solution
k = {10.800900828, -0.300900828}