3k^2+2k-40=0

Solution for 3k^2+2k-40=0 equation:

Simplifying
3k2 + 2k + -40 = 0

Reorder the terms:
-40 + 2k + 3k2 = 0

Solving
-40 + 2k + 3k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-4 + -1k)(10 + -3k) = 0

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

Simplifying
-4 + -1k = 0

Solving
-4 + -1k = 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 + -1k = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1k = 0 + 4
-1k = 0 + 4

Combine like terms: 0 + 4 = 4
-1k = 4

Divide each side by '-1'.
k = -4

Simplifying
k = -4
Subproblem 2
Set the factor '(10 + -3k)' equal to zero and attempt to solve:

Simplifying
10 + -3k = 0

Solving
10 + -3k = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3k = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3k = 0 + -10
-3k = 0 + -10

Combine like terms: 0 + -10 = -10
-3k = -10

Divide each side by '-3'.
k = 3.333333333

Simplifying
k = 3.333333333
Solution
k = {-4, 3.333333333}