18k^2-12k=2+4k^2

Solution for 18k^2-12k=2+4k^2 equation:

Simplifying
18k2 + -12k = 2 + 4k2

Reorder the terms:
-12k + 18k2 = 2 + 4k2

Solving
-12k + 18k2 = 2 + 4k2

Solving for variable 'k'.

Reorder the terms:
-2 + -12k + 18k2 + -4k2 = 2 + 4k2 + -2 + -4k2

Combine like terms: 18k2 + -4k2 = 14k2
-2 + -12k + 14k2 = 2 + 4k2 + -2 + -4k2

Reorder the terms:
-2 + -12k + 14k2 = 2 + -2 + 4k2 + -4k2

Combine like terms: 2 + -2 = 0
-2 + -12k + 14k2 = 0 + 4k2 + -4k2
-2 + -12k + 14k2 = 4k2 + -4k2

Combine like terms: 4k2 + -4k2 = 0
-2 + -12k + 14k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -6k + 7k2) = 0

Factor a trinomial.
2((-1 + -7k)(1 + -1k)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -7k)' equal to zero and attempt to solve:

Simplifying
-1 + -7k = 0

Solving
-1 + -7k = 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 + -7k = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7k = 0 + 1
-7k = 0 + 1

Combine like terms: 0 + 1 = 1
-7k = 1

Divide each side by '-7'.
k = -0.1428571429

Simplifying
k = -0.1428571429
Subproblem 2
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
Solution
k = {-0.1428571429, 1}