2j^2-5j-3=0

Solution for 2j^2-5j-3=0 equation:

Simplifying
2j2 + -5j + -3 = 0

Reorder the terms:
-3 + -5j + 2j2 = 0

Solving
-3 + -5j + 2j2 = 0

Solving for variable 'j'.

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

Subproblem 1
Set the factor '(-1 + -2j)' equal to zero and attempt to solve:

Simplifying
-1 + -2j = 0

Solving
-1 + -2j = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2j = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2j = 0 + 1
-2j = 0 + 1

Combine like terms: 0 + 1 = 1
-2j = 1

Divide each side by '-2'.
j = -0.5

Simplifying
j = -0.5
Subproblem 2
Set the factor '(3 + -1j)' equal to zero and attempt to solve:

Simplifying
3 + -1j = 0

Solving
3 + -1j = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1j = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1j = 0 + -3
-1j = 0 + -3

Combine like terms: 0 + -3 = -3
-1j = -3

Divide each side by '-1'.
j = 3

Simplifying
j = 3
Solution
j = {-0.5, 3}