4k^2-6=k^2+17k

Solution for 4k^2-6=k^2+17k equation:

Simplifying
4k2 + -6 = k2 + 17k

Reorder the terms:
-6 + 4k2 = k2 + 17k

Reorder the terms:
-6 + 4k2 = 17k + k2

Solving
-6 + 4k2 = 17k + k2

Solving for variable 'k'.

Reorder the terms:
-6 + -17k + 4k2 + -1k2 = 17k + k2 + -17k + -1k2

Combine like terms: 4k2 + -1k2 = 3k2
-6 + -17k + 3k2 = 17k + k2 + -17k + -1k2

Reorder the terms:
-6 + -17k + 3k2 = 17k + -17k + k2 + -1k2

Combine like terms: 17k + -17k = 0
-6 + -17k + 3k2 = 0 + k2 + -1k2
-6 + -17k + 3k2 = k2 + -1k2

Combine like terms: k2 + -1k2 = 0
-6 + -17k + 3k2 = 0

Factor a trinomial.
(-1 + -3k)(6 + -1k) = 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 '(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 = {-0.3333333333, 6}