j^2-18j-19=0

Solution for j^2-18j-19=0 equation:

Simplifying
j2 + -18j + -19 = 0

Reorder the terms:
-19 + -18j + j2 = 0

Solving
-19 + -18j + j2 = 0

Solving for variable 'j'.

Factor a trinomial.
(-1 + -1j)(19 + -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 '(19 + -1j)' equal to zero and attempt to solve:

Simplifying
19 + -1j = 0

Solving
19 + -1j = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1j = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1j = 0 + -19
-1j = 0 + -19

Combine like terms: 0 + -19 = -19
-1j = -19

Divide each side by '-1'.
j = 19

Simplifying
j = 19
Solution
j = {-1, 19}