21k^2-19k=12

Solution for 21k^2-19k=12 equation:

Simplifying
21k2 + -19k = 12

Reorder the terms:
-19k + 21k2 = 12

Solving
-19k + 21k2 = 12

Solving for variable 'k'.

Reorder the terms:
-12 + -19k + 21k2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -19k + 21k2 = 0

Factor a trinomial.
(-3 + -7k)(4 + -3k) = 0

Subproblem 1
Set the factor '(-3 + -7k)' equal to zero and attempt to solve:

Simplifying
-3 + -7k = 0

Solving
-3 + -7k = 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 + -7k = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7k = 0 + 3
-7k = 0 + 3

Combine like terms: 0 + 3 = 3
-7k = 3

Divide each side by '-7'.
k = -0.4285714286

Simplifying
k = -0.4285714286
Subproblem 2
Set the factor '(4 + -3k)' equal to zero and attempt to solve:

Simplifying
4 + -3k = 0

Solving
4 + -3k = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3k = 0 + -4
-3k = 0 + -4

Combine like terms: 0 + -4 = -4
-3k = -4

Divide each side by '-3'.
k = 1.333333333

Simplifying
k = 1.333333333
Solution
k = {-0.4285714286, 1.333333333}