-2k^2-7k-3=0

Solution for -2k^2-7k-3=0 equation:

Simplifying
-2k2 + -7k + -3 = 0

Reorder the terms:
-3 + -7k + -2k2 = 0

Solving
-3 + -7k + -2k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 7k + 2k2) = 0

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

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

Simplifying
3 + k = 0

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

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

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

Simplifying
k = -3
Subproblem 2
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
Solution
k = {-3, -0.5}