(4j+5)(j+6)=0

Solution for (4j+5)(j+6)=0 equation:

Simplifying
(4j + 5)(j + 6) = 0

Reorder the terms:
(5 + 4j)(j + 6) = 0

Reorder the terms:
(5 + 4j)(6 + j) = 0

Multiply (5 + 4j) * (6 + j)
(5(6 + j) + 4j * (6 + j)) = 0
((6 * 5 + j * 5) + 4j * (6 + j)) = 0
((30 + 5j) + 4j * (6 + j)) = 0
(30 + 5j + (6 * 4j + j * 4j)) = 0
(30 + 5j + (24j + 4j2)) = 0

Combine like terms: 5j + 24j = 29j
(30 + 29j + 4j2) = 0

Solving
30 + 29j + 4j2 = 0

Solving for variable 'j'.

Factor a trinomial.
(6 + j)(5 + 4j) = 0

Subproblem 1
Set the factor '(6 + j)' equal to zero and attempt to solve:

Simplifying
6 + j = 0

Solving
6 + j = 0

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

Add '-6' to each side of the equation.
6 + -6 + j = 0 + -6

Combine like terms: 6 + -6 = 0
0 + j = 0 + -6
j = 0 + -6

Combine like terms: 0 + -6 = -6
j = -6

Simplifying
j = -6
Subproblem 2
Set the factor '(5 + 4j)' equal to zero and attempt to solve:

Simplifying
5 + 4j = 0

Solving
5 + 4j = 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 + 4j = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4j = 0 + -5
4j = 0 + -5

Combine like terms: 0 + -5 = -5
4j = -5

Divide each side by '4'.
j = -1.25

Simplifying
j = -1.25
Solution
j = {-6, -1.25}