7k^2+10k+3=0

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

Simplifying
7k2 + 10k + 3 = 0

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

Solving
3 + 10k + 7k2 = 0

Solving for variable 'k'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(3 + 7k)' equal to zero and attempt to solve:

Simplifying
3 + 7k = 0

Solving
3 + 7k = 0

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

Add '-3' to each side of the equation.
3 + -3 + 7k = 0 + -3

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

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

Divide each side by '7'.
k = -0.4285714286

Simplifying
k = -0.4285714286
Solution
k = {-1, -0.4285714286}