3(k-2)-6=4k(3k-1)

Solution for 3(k-2)-6=4k(3k-1) equation:

Simplifying
3(k + -2) + -6 = 4k(3k + -1)

Reorder the terms:
3(-2 + k) + -6 = 4k(3k + -1)
(-2 * 3 + k * 3) + -6 = 4k(3k + -1)
(-6 + 3k) + -6 = 4k(3k + -1)

Reorder the terms:
-6 + -6 + 3k = 4k(3k + -1)

Combine like terms: -6 + -6 = -12
-12 + 3k = 4k(3k + -1)

Reorder the terms:
-12 + 3k = 4k(-1 + 3k)
-12 + 3k = (-1 * 4k + 3k * 4k)
-12 + 3k = (-4k + 12k2)

Solving
-12 + 3k = -4k + 12k2

Solving for variable 'k'.

Combine like terms: 3k + 4k = 7k
-12 + 7k + -12k2 = -4k + 12k2 + 4k + -12k2

Reorder the terms:
-12 + 7k + -12k2 = -4k + 4k + 12k2 + -12k2

Combine like terms: -4k + 4k = 0
-12 + 7k + -12k2 = 0 + 12k2 + -12k2
-12 + 7k + -12k2 = 12k2 + -12k2

Combine like terms: 12k2 + -12k2 = 0
-12 + 7k + -12k2 = 0

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

Divide each side by '-12'.
1 + -0.5833333333k + k2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -0.5833333333k + -1 + k2 = 0 + -1

Reorder the terms:
1 + -1 + -0.5833333333k + k2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -0.5833333333k + k2 = 0 + -1
-0.5833333333k + k2 = 0 + -1

Combine like terms: 0 + -1 = -1
-0.5833333333k + k2 = -1

The k term is -0.5833333333k.  Take half its coefficient (-0.2916666667).
Square it (0.08506944446) and add it to both sides.

Add '0.08506944446' to each side of the equation.
-0.5833333333k + 0.08506944446 + k2 = -1 + 0.08506944446

Reorder the terms:
0.08506944446 + -0.5833333333k + k2 = -1 + 0.08506944446

Combine like terms: -1 + 0.08506944446 = -0.91493055554
0.08506944446 + -0.5833333333k + k2 = -0.91493055554

Factor a perfect square on the left side:
(k + -0.2916666667)(k + -0.2916666667) = -0.91493055554

Can't calculate square root of the right side.

The solution to this equation could not be determined.