j^2-19j-20=0

Solution for j^2-19j-20=0 equation:

Simplifying
j2 + -19j + -20 = 0

Reorder the terms:
-20 + -19j + j2 = 0

Solving
-20 + -19j + j2 = 0

Solving for variable 'j'.

Factor a trinomial.
(-1 + -1j)(20 + -1j) = 0

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

Simplifying
-1 + -1j = 0

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

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

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

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

Simplifying
j = -1
Subproblem 2
Set the factor '(20 + -1j)' equal to zero and attempt to solve:

Simplifying
20 + -1j = 0

Solving
20 + -1j = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1j = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1j = 0 + -20
-1j = 0 + -20

Combine like terms: 0 + -20 = -20
-1j = -20

Divide each side by '-1'.
j = 20

Simplifying
j = 20
Solution
j = {-1, 20}