4k^2-4k=6+2k^2

Solution for 4k^2-4k=6+2k^2 equation:

Simplifying
4k2 + -4k = 6 + 2k2

Reorder the terms:
-4k + 4k2 = 6 + 2k2

Solving
-4k + 4k2 = 6 + 2k2

Solving for variable 'k'.

Reorder the terms:
-6 + -4k + 4k2 + -2k2 = 6 + 2k2 + -6 + -2k2

Combine like terms: 4k2 + -2k2 = 2k2
-6 + -4k + 2k2 = 6 + 2k2 + -6 + -2k2

Reorder the terms:
-6 + -4k + 2k2 = 6 + -6 + 2k2 + -2k2

Combine like terms: 6 + -6 = 0
-6 + -4k + 2k2 = 0 + 2k2 + -2k2
-6 + -4k + 2k2 = 2k2 + -2k2

Combine like terms: 2k2 + -2k2 = 0
-6 + -4k + 2k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -2k + k2) = 0

Factor a trinomial.
2((-1 + -1k)(3 + -1k)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -1k)' equal to zero and attempt to solve:

Simplifying
-1 + -1k = 0

Solving
-1 + -1k = 0

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

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

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

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

Divide each side by '-1'.
k = -1

Simplifying
k = -1
Subproblem 2
Set the factor '(3 + -1k)' equal to zero and attempt to solve:

Simplifying
3 + -1k = 0

Solving
3 + -1k = 0

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

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

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

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

Divide each side by '-1'.
k = 3

Simplifying
k = 3
Solution
k = {-1, 3}