j^2-3j-10=0

Solution for j^2-3j-10=0 equation:

Simplifying
j2 + -3j + -10 = 0

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

Solving
-10 + -3j + j2 = 0

Solving for variable 'j'.

Factor a trinomial.
(-2 + -1j)(5 + -1j) = 0

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

Simplifying
-2 + -1j = 0

Solving
-2 + -1j = 0

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

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

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

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

Divide each side by '-1'.
j = -2

Simplifying
j = -2
Subproblem 2
Set the factor '(5 + -1j)' equal to zero and attempt to solve:

Simplifying
5 + -1j = 0

Solving
5 + -1j = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1j = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1j = 0 + -5
-1j = 0 + -5

Combine like terms: 0 + -5 = -5
-1j = -5

Divide each side by '-1'.
j = 5

Simplifying
j = 5
Solution
j = {-2, 5}