2k^2=19k-42

Solution for 2k^2=19k-42 equation:

Simplifying
2k2 = 19k + -42

Reorder the terms:
2k2 = -42 + 19k

Solving
2k2 = -42 + 19k

Solving for variable 'k'.

Reorder the terms:
42 + -19k + 2k2 = -42 + 19k + 42 + -19k

Reorder the terms:
42 + -19k + 2k2 = -42 + 42 + 19k + -19k

Combine like terms: -42 + 42 = 0
42 + -19k + 2k2 = 0 + 19k + -19k
42 + -19k + 2k2 = 19k + -19k

Combine like terms: 19k + -19k = 0
42 + -19k + 2k2 = 0

Factor a trinomial.
(7 + -2k)(6 + -1k) = 0

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

Simplifying
7 + -2k = 0

Solving
7 + -2k = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2k = 0 + -7
-2k = 0 + -7

Combine like terms: 0 + -7 = -7
-2k = -7

Divide each side by '-2'.
k = 3.5

Simplifying
k = 3.5
Subproblem 2
Set the factor '(6 + -1k)' equal to zero and attempt to solve:

Simplifying
6 + -1k = 0

Solving
6 + -1k = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1k = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1k = 0 + -6
-1k = 0 + -6

Combine like terms: 0 + -6 = -6
-1k = -6

Divide each side by '-1'.
k = 6

Simplifying
k = 6
Solution
k = {3.5, 6}