j^2+4j-45=0

Solution for j^2+4j-45=0 equation:

Simplifying
j2 + 4j + -45 = 0

Reorder the terms:
-45 + 4j + j2 = 0

Solving
-45 + 4j + j2 = 0

Solving for variable 'j'.

Factor a trinomial.
(-9 + -1j)(5 + -1j) = 0

Subproblem 1
Set the factor '(-9 + -1j)' equal to zero and attempt to solve:

Simplifying
-9 + -1j = 0

Solving
-9 + -1j = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1j = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1j = 0 + 9
-1j = 0 + 9

Combine like terms: 0 + 9 = 9
-1j = 9

Divide each side by '-1'.
j = -9

Simplifying
j = -9
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 = {-9, 5}