21-8k-2k^2=2k^2

Solution for 21-8k-2k^2=2k^2 equation:

Simplifying
21 + -8k + -2k2 = 2k2

Solving
21 + -8k + -2k2 = 2k2

Solving for variable 'k'.

Combine like terms: -2k2 + -2k2 = -4k2
21 + -8k + -4k2 = 2k2 + -2k2

Combine like terms: 2k2 + -2k2 = 0
21 + -8k + -4k2 = 0

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

Subproblem 1
Set the factor '(3 + -2k)' equal to zero and attempt to solve:

Simplifying
3 + -2k = 0

Solving
3 + -2k = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2k = 0 + -3
-2k = 0 + -3

Combine like terms: 0 + -3 = -3
-2k = -3

Divide each side by '-2'.
k = 1.5

Simplifying
k = 1.5
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 = {1.5, -3.5}