12k^2-5k=2

Solution for 12k^2-5k=2 equation:

Simplifying
12k2 + -5k = 2

Reorder the terms:
-5k + 12k2 = 2

Solving
-5k + 12k2 = 2

Solving for variable 'k'.

Reorder the terms:
-2 + -5k + 12k2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -5k + 12k2 = 0

Factor a trinomial.
(-1 + -4k)(2 + -3k) = 0

Subproblem 1
Set the factor '(-1 + -4k)' equal to zero and attempt to solve:

Simplifying
-1 + -4k = 0

Solving
-1 + -4k = 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 + -4k = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4k = 0 + 1
-4k = 0 + 1

Combine like terms: 0 + 1 = 1
-4k = 1

Divide each side by '-4'.
k = -0.25

Simplifying
k = -0.25
Subproblem 2
Set the factor '(2 + -3k)' equal to zero and attempt to solve:

Simplifying
2 + -3k = 0

Solving
2 + -3k = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3k = 0 + -2
-3k = 0 + -2

Combine like terms: 0 + -2 = -2
-3k = -2

Divide each side by '-3'.
k = 0.6666666667

Simplifying
k = 0.6666666667
Solution
k = {-0.25, 0.6666666667}