8k^2=-168+80k

Solution for 8k^2=-168+80k equation:

Simplifying
8k2 = -168 + 80k

Solving
8k2 = -168 + 80k

Solving for variable 'k'.

Reorder the terms:
168 + -80k + 8k2 = -168 + 80k + 168 + -80k

Reorder the terms:
168 + -80k + 8k2 = -168 + 168 + 80k + -80k

Combine like terms: -168 + 168 = 0
168 + -80k + 8k2 = 0 + 80k + -80k
168 + -80k + 8k2 = 80k + -80k

Combine like terms: 80k + -80k = 0
168 + -80k + 8k2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(21 + -10k + k2) = 0

Factor a trinomial.
8((3 + -1k)(7 + -1k)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(3 + -1k)' equal to zero and attempt to solve:

Simplifying
3 + -1k = 0

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

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

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

Divide each side by '-1'.
k = 3

Simplifying
k = 3
Subproblem 2
Set the factor '(7 + -1k)' equal to zero and attempt to solve:

Simplifying
7 + -1k = 0

Solving
7 + -1k = 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 + -1k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1k = 0 + -7
-1k = 0 + -7

Combine like terms: 0 + -7 = -7
-1k = -7

Divide each side by '-1'.
k = 7

Simplifying
k = 7
Solution
k = {3, 7}