2x^2+5kx+3k^2=0

Solution for 2x^2+5kx+3k^2=0 equation:

Simplifying
2x2 + 5kx + 3k2 = 0

Reorder the terms:
5kx + 3k2 + 2x2 = 0

Solving
5kx + 3k2 + 2x2 = 0

Solving for variable 'k'.

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

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

Simplifying
3k + 2x = 0

Solving
3k + 2x = 0

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

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

Combine like terms: 2x + -2x = 0
3k + 0 = 0 + -2x
3k = 0 + -2x
Remove the zero:
3k = -2x

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

Simplifying
k = -0.6666666667x
Subproblem 2
Set the factor '(k + x)' equal to zero and attempt to solve:

Simplifying
k + x = 0

Solving
k + x = 0

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

Add '-1x' to each side of the equation.
k + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
k + 0 = 0 + -1x
k = 0 + -1x
Remove the zero:
k = -1x

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