-j^2+20j-75=0

Solution for -j^2+20j-75=0 equation:

Simplifying
-1j2 + 20j + -75 = 0

Reorder the terms:
-75 + 20j + -1j2 = 0

Solving
-75 + 20j + -1j2 = 0

Solving for variable 'j'.

Factor a trinomial.
(-15 + j)(5 + -1j) = 0

Subproblem 1
Set the factor '(-15 + j)' equal to zero and attempt to solve:

Simplifying
-15 + j = 0

Solving
-15 + j = 0

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

Add '15' to each side of the equation.
-15 + 15 + j = 0 + 15

Combine like terms: -15 + 15 = 0
0 + j = 0 + 15
j = 0 + 15

Combine like terms: 0 + 15 = 15
j = 15

Simplifying
j = 15
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 = {15, 5}