2j^2+2j+3j=3

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

Simplifying
2j2 + 2j + 3j = 3

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

Combine like terms: 2j + 3j = 5j
5j + 2j2 = 3

Solving
5j + 2j2 = 3

Solving for variable 'j'.

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

Combine like terms: 3 + -3 = 0
-3 + 5j + 2j2 = 0

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

Subproblem 1
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
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 = {-3, 0.5}