42k^2+35k+7=0

Solution for 42k^2+35k+7=0 equation:

Simplifying
42k2 + 35k + 7 = 0

Reorder the terms:
7 + 35k + 42k2 = 0

Solving
7 + 35k + 42k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '7'.
7(1 + 5k + 6k2) = 0

Factor a trinomial.
7((1 + 2k)(1 + 3k)) = 0

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

Simplifying
1 + 2k = 0

Solving
1 + 2k = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2k = 0 + -1
2k = 0 + -1

Combine like terms: 0 + -1 = -1
2k = -1

Divide each side by '2'.
k = -0.5

Simplifying
k = -0.5
Subproblem 2
Set the factor '(1 + 3k)' equal to zero and attempt to solve:

Simplifying
1 + 3k = 0

Solving
1 + 3k = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3k = 0 + -1

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

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

Divide each side by '3'.
k = -0.3333333333

Simplifying
k = -0.3333333333
Solution
k = {-0.5, -0.3333333333}