3k^2+5k=-2

Solution for 3k^2+5k=-2 equation:

Simplifying
3k2 + 5k = -2

Reorder the terms:
5k + 3k2 = -2

Solving
5k + 3k2 = -2

Solving for variable 'k'.

Reorder the terms:
2 + 5k + 3k2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + 5k + 3k2 = 0

Factor a trinomial.
(1 + k)(2 + 3k) = 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 '(2 + 3k)' equal to zero and attempt to solve:

Simplifying
2 + 3k = 0

Solving
2 + 3k = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3k = 0 + -2
3k = 0 + -2

Combine like terms: 0 + -2 = -2
3k = -2

Divide each side by '3'.
k = -0.6666666667

Simplifying
k = -0.6666666667
Solution
k = {-1, -0.6666666667}