12k^2+8k-3=0

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Solution for 12k^2+8k-3=0 equation: 


Simplifying
12k2 + 8k + -3 = 0

Reorder the terms:
-3 + 8k + 12k2 = 0

Solving
-3 + 8k + 12k2 = 0

Solving for variable 'k'.

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

Divide each side by '12'.
-0.25 + 0.6666666667k + k2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 0.6666666667k + 0.25 + k2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 0.6666666667k + k2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 0.6666666667k + k2 = 0 + 0.25
0.6666666667k + k2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
0.6666666667k + k2 = 0.25

The k term is 0.6666666667k.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667k + 0.1111111112 + k2 = 0.25 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667k + k2 = 0.25 + 0.1111111112

Combine like terms: 0.25 + 0.1111111112 = 0.3611111112
0.1111111112 + 0.6666666667k + k2 = 0.3611111112

Factor a perfect square on the left side:
(k + 0.3333333334)(k + 0.3333333334) = 0.3611111112

Calculate the square root of the right side: 0.600925213

Break this problem into two subproblems by setting 
(k + 0.3333333334) equal to 0.600925213 and -0.600925213.


Subproblem 1
k + 0.3333333334 = 0.600925213

Simplifying
k + 0.3333333334 = 0.600925213

Reorder the terms:
0.3333333334 + k = 0.600925213

Solving
0.3333333334 + k = 0.600925213

Solving for variable 'k'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + k = 0.600925213 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + k = 0.600925213 + -0.3333333334
k = 0.600925213 + -0.3333333334

Combine like terms: 0.600925213 + -0.3333333334 = 0.2675918796
k = 0.2675918796

Simplifying
k = 0.2675918796


Subproblem 2
k + 0.3333333334 = -0.600925213

Simplifying
k + 0.3333333334 = -0.600925213

Reorder the terms:
0.3333333334 + k = -0.600925213

Solving
0.3333333334 + k = -0.600925213

Solving for variable 'k'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + k = -0.600925213 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + k = -0.600925213 + -0.3333333334
k = -0.600925213 + -0.3333333334

Combine like terms: -0.600925213 + -0.3333333334 = -0.9342585464
k = -0.9342585464

Simplifying
k = -0.9342585464


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.2675918796, -0.9342585464}

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