3k^2+31k+70=0

Solution for 3k^2+31k+70=0 equation:

Simplifying
3k2 + 31k + 70 = 0

Reorder the terms:
70 + 31k + 3k2 = 0

Solving
70 + 31k + 3k2 = 0

Solving for variable 'k'.

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

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

Simplifying
7 + k = 0

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

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

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

Simplifying
k = -7
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 = {-7, -3.333333333}