2k^2-11k=105

Solution for 2k^2-11k=105 equation:

Simplifying
2k2 + -11k = 105

Reorder the terms:
-11k + 2k2 = 105

Solving
-11k + 2k2 = 105

Solving for variable 'k'.

Reorder the terms:
-105 + -11k + 2k2 = 105 + -105

Combine like terms: 105 + -105 = 0
-105 + -11k + 2k2 = 0

Factor a trinomial.
(-5 + -1k)(21 + -2k) = 0

Subproblem 1
Set the factor '(-5 + -1k)' equal to zero and attempt to solve:

Simplifying
-5 + -1k = 0

Solving
-5 + -1k = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1k = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1k = 0 + 5
-1k = 0 + 5

Combine like terms: 0 + 5 = 5
-1k = 5

Divide each side by '-1'.
k = -5

Simplifying
k = -5
Subproblem 2
Set the factor '(21 + -2k)' equal to zero and attempt to solve:

Simplifying
21 + -2k = 0

Solving
21 + -2k = 0

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

Add '-21' to each side of the equation.
21 + -21 + -2k = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -2k = 0 + -21
-2k = 0 + -21

Combine like terms: 0 + -21 = -21
-2k = -21

Divide each side by '-2'.
k = 10.5

Simplifying
k = 10.5
Solution
k = {-5, 10.5}