5j(j-4)=3(4-j)

Solution for 5j(j-4)=3(4-j) equation:

Simplifying
5j(j + -4) = 3(4 + -1j)

Reorder the terms:
5j(-4 + j) = 3(4 + -1j)
(-4 * 5j + j * 5j) = 3(4 + -1j)
(-20j + 5j2) = 3(4 + -1j)
-20j + 5j2 = (4 * 3 + -1j * 3)
-20j + 5j2 = (12 + -3j)

Solving
-20j + 5j2 = 12 + -3j

Solving for variable 'j'.

Reorder the terms:
-12 + -20j + 3j + 5j2 = 12 + -3j + -12 + 3j

Combine like terms: -20j + 3j = -17j
-12 + -17j + 5j2 = 12 + -3j + -12 + 3j

Reorder the terms:
-12 + -17j + 5j2 = 12 + -12 + -3j + 3j

Combine like terms: 12 + -12 = 0
-12 + -17j + 5j2 = 0 + -3j + 3j
-12 + -17j + 5j2 = -3j + 3j

Combine like terms: -3j + 3j = 0
-12 + -17j + 5j2 = 0

Factor a trinomial.
(-3 + -5j)(4 + -1j) = 0

Subproblem 1
Set the factor '(-3 + -5j)' equal to zero and attempt to solve:

Simplifying
-3 + -5j = 0

Solving
-3 + -5j = 0

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

Add '3' to each side of the equation.
-3 + 3 + -5j = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5j = 0 + 3
-5j = 0 + 3

Combine like terms: 0 + 3 = 3
-5j = 3

Divide each side by '-5'.
j = -0.6

Simplifying
j = -0.6
Subproblem 2
Set the factor '(4 + -1j)' equal to zero and attempt to solve:

Simplifying
4 + -1j = 0

Solving
4 + -1j = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1j = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1j = 0 + -4
-1j = 0 + -4

Combine like terms: 0 + -4 = -4
-1j = -4

Divide each side by '-1'.
j = 4

Simplifying
j = 4
Solution
j = {-0.6, 4}