3k^2+10k+7=0

Solution for 3k^2+10k+7=0 equation:

Simplifying
3k2 + 10k + 7 = 0

Reorder the terms:
7 + 10k + 3k2 = 0

Solving
7 + 10k + 3k2 = 0

Solving for variable 'k'.

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

Subproblem 1
Set the factor '(7 + 3k)' equal to zero and attempt to solve:

Simplifying
7 + 3k = 0

Solving
7 + 3k = 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 + 3k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3k = 0 + -7
3k = 0 + -7

Combine like terms: 0 + -7 = -7
3k = -7

Divide each side by '3'.
k = -2.333333333

Simplifying
k = -2.333333333
Subproblem 2
Set the factor '(1 + k)' equal to zero and attempt to solve:

Simplifying
1 + k = 0

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

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

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

Simplifying
k = -1
Solution
k = {-2.333333333, -1}