3j^2+31j+10=0

Solution for 3j^2+31j+10=0 equation:

Simplifying
3j2 + 31j + 10 = 0

Reorder the terms:
10 + 31j + 3j2 = 0

Solving
10 + 31j + 3j2 = 0

Solving for variable 'j'.

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

Subproblem 1
Set the factor '(10 + j)' equal to zero and attempt to solve:

Simplifying
10 + j = 0

Solving
10 + j = 0

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

Add '-10' to each side of the equation.
10 + -10 + j = 0 + -10

Combine like terms: 10 + -10 = 0
0 + j = 0 + -10
j = 0 + -10

Combine like terms: 0 + -10 = -10
j = -10

Simplifying
j = -10
Subproblem 2
Set the factor '(1 + 3j)' equal to zero and attempt to solve:

Simplifying
1 + 3j = 0

Solving
1 + 3j = 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 + 3j = 0 + -1

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

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

Divide each side by '3'.
j = -0.3333333333

Simplifying
j = -0.3333333333
Solution
j = {-10, -0.3333333333}