j^2-20j+75=0

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

Simplifying
j2 + -20j + 75 = 0

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

Solving
75 + -20j + j2 = 0

Solving for variable 'j'.

Factor a trinomial.
(5 + -1j)(15 + -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 '(15 + -1j)' equal to zero and attempt to solve:

Simplifying
15 + -1j = 0

Solving
15 + -1j = 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 + -1j = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1j = 0 + -15
-1j = 0 + -15

Combine like terms: 0 + -15 = -15
-1j = -15

Divide each side by '-1'.
j = 15

Simplifying
j = 15
Solution
j = {5, 15}