30k^2-74k+40=0

Solution for 30k^2-74k+40=0 equation:

Simplifying
30k2 + -74k + 40 = 0

Reorder the terms:
40 + -74k + 30k2 = 0

Solving
40 + -74k + 30k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + -37k + 15k2) = 0

Factor a trinomial.
2((4 + -5k)(5 + -3k)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -5k)' equal to zero and attempt to solve:

Simplifying
4 + -5k = 0

Solving
4 + -5k = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5k = 0 + -4
-5k = 0 + -4

Combine like terms: 0 + -4 = -4
-5k = -4

Divide each side by '-5'.
k = 0.8

Simplifying
k = 0.8
Subproblem 2
Set the factor '(5 + -3k)' equal to zero and attempt to solve:

Simplifying
5 + -3k = 0

Solving
5 + -3k = 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 + -3k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3k = 0 + -5
-3k = 0 + -5

Combine like terms: 0 + -5 = -5
-3k = -5

Divide each side by '-3'.
k = 1.666666667

Simplifying
k = 1.666666667
Solution
k = {0.8, 1.666666667}