6k^2-7=19k

Solution for 6k^2-7=19k equation:

Simplifying
6k2 + -7 = 19k

Reorder the terms:
-7 + 6k2 = 19k

Solving
-7 + 6k2 = 19k

Solving for variable 'k'.

Reorder the terms:
-7 + -19k + 6k2 = 19k + -19k

Combine like terms: 19k + -19k = 0
-7 + -19k + 6k2 = 0

Factor a trinomial.
(-1 + -3k)(7 + -2k) = 0

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

Simplifying
-1 + -3k = 0

Solving
-1 + -3k = 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 + -3k = 0 + 1

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

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

Divide each side by '-3'.
k = -0.3333333333

Simplifying
k = -0.3333333333
Subproblem 2
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
Solution
k = {-0.3333333333, 3.5}