80k^2-116k+42=0

Solution for 80k^2-116k+42=0 equation:

Simplifying
80k2 + -116k + 42 = 0

Reorder the terms:
42 + -116k + 80k2 = 0

Solving
42 + -116k + 80k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + -58k + 40k2) = 0

Factor a trinomial.
2((7 + -10k)(3 + -4k)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + -10k)' equal to zero and attempt to solve:

Simplifying
7 + -10k = 0

Solving
7 + -10k = 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 + -10k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -10k = 0 + -7
-10k = 0 + -7

Combine like terms: 0 + -7 = -7
-10k = -7

Divide each side by '-10'.
k = 0.7

Simplifying
k = 0.7
Subproblem 2
Set the factor '(3 + -4k)' equal to zero and attempt to solve:

Simplifying
3 + -4k = 0

Solving
3 + -4k = 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 + -4k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4k = 0 + -3
-4k = 0 + -3

Combine like terms: 0 + -3 = -3
-4k = -3

Divide each side by '-4'.
k = 0.75

Simplifying
k = 0.75
Solution
k = {0.7, 0.75}