6k^2+34k=-k+6

Solution for 6k^2+34k=-k+6 equation:

Simplifying
6k2 + 34k = -1k + 6

Reorder the terms:
34k + 6k2 = -1k + 6

Reorder the terms:
34k + 6k2 = 6 + -1k

Solving
34k + 6k2 = 6 + -1k

Solving for variable 'k'.

Reorder the terms:
-6 + 34k + k + 6k2 = 6 + -1k + -6 + k

Combine like terms: 34k + k = 35k
-6 + 35k + 6k2 = 6 + -1k + -6 + k

Reorder the terms:
-6 + 35k + 6k2 = 6 + -6 + -1k + k

Combine like terms: 6 + -6 = 0
-6 + 35k + 6k2 = 0 + -1k + k
-6 + 35k + 6k2 = -1k + k

Combine like terms: -1k + k = 0
-6 + 35k + 6k2 = 0

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

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

Simplifying
1 + -6k = 0

Solving
1 + -6k = 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 + -6k = 0 + -1

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

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

Divide each side by '-6'.
k = 0.1666666667

Simplifying
k = 0.1666666667
Solution
k = {-6, 0.1666666667}