(j-6)(9j-7)=0

Solution for (j-6)(9j-7)=0 equation:

Simplifying
(j + -6)(9j + -7) = 0

Reorder the terms:
(-6 + j)(9j + -7) = 0

Reorder the terms:
(-6 + j)(-7 + 9j) = 0

Multiply (-6 + j) * (-7 + 9j)
(-6(-7 + 9j) + j(-7 + 9j)) = 0
((-7 * -6 + 9j * -6) + j(-7 + 9j)) = 0
((42 + -54j) + j(-7 + 9j)) = 0
(42 + -54j + (-7 * j + 9j * j)) = 0
(42 + -54j + (-7j + 9j2)) = 0

Combine like terms: -54j + -7j = -61j
(42 + -61j + 9j2) = 0

Solving
42 + -61j + 9j2 = 0

Solving for variable 'j'.

Factor a trinomial.
(7 + -9j)(6 + -1j) = 0

Subproblem 1
Set the factor '(7 + -9j)' equal to zero and attempt to solve:

Simplifying
7 + -9j = 0

Solving
7 + -9j = 0

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

Add '-7' to each side of the equation.
7 + -7 + -9j = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -9j = 0 + -7
-9j = 0 + -7

Combine like terms: 0 + -7 = -7
-9j = -7

Divide each side by '-9'.
j = 0.7777777778

Simplifying
j = 0.7777777778
Subproblem 2
Set the factor '(6 + -1j)' equal to zero and attempt to solve:

Simplifying
6 + -1j = 0

Solving
6 + -1j = 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 + -1j = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1j = 0 + -6
-1j = 0 + -6

Combine like terms: 0 + -6 = -6
-1j = -6

Divide each side by '-1'.
j = 6

Simplifying
j = 6
Solution
j = {0.7777777778, 6}