j^2+j-20=0

Solution for j^2+j-20=0 equation:

Simplifying
j2 + j + -20 = 0

Reorder the terms:
-20 + j + j2 = 0

Solving
-20 + j + j2 = 0

Solving for variable 'j'.

Factor a trinomial.
(-5 + -1j)(4 + -1j) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1j)' equal to zero and attempt to solve:

Simplifying
4 + -1j = 0

Solving
4 + -1j = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1j = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1j = 0 + -4
-1j = 0 + -4

Combine like terms: 0 + -4 = -4
-1j = -4

Divide each side by '-1'.
j = 4

Simplifying
j = 4
Solution
j = {-5, 4}