2j^2+3j=-1

Solution for 2j^2+3j=-1 equation:

Simplifying
2j2 + 3j = -1

Reorder the terms:
3j + 2j2 = -1

Solving
3j + 2j2 = -1

Solving for variable 'j'.

Reorder the terms:
1 + 3j + 2j2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + 3j + 2j2 = 0

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

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

Simplifying
1 + j = 0

Solving
1 + j = 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 + j = 0 + -1

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

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

Simplifying
j = -1
Subproblem 2
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
Solution
j = {-1, -0.5}