(5-8ix)(1-3ix)=

Solution for (5-8ix)(1-3ix)= equation:

Simplifying
(5 + -8ix)(1 + -3ix) = 0

Multiply (5 + -8ix) * (1 + -3ix)
(5(1 + -3ix) + -8ix * (1 + -3ix)) = 0
((1 * 5 + -3ix * 5) + -8ix * (1 + -3ix)) = 0
((5 + -15ix) + -8ix * (1 + -3ix)) = 0
(5 + -15ix + (1 * -8ix + -3ix * -8ix)) = 0
(5 + -15ix + (-8ix + 24i2x2)) = 0

Combine like terms: -15ix + -8ix = -23ix
(5 + -23ix + 24i2x2) = 0

Solving
5 + -23ix + 24i2x2 = 0

Solving for variable 'i'.

Factor a trinomial.
(1 + -3ix)(5 + -8ix) = 0

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

Simplifying
1 + -3ix = 0

Solving
1 + -3ix = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3ix = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3ix = 0 + -1
-3ix = 0 + -1

Combine like terms: 0 + -1 = -1
-3ix = -1

Divide each side by '-3x'.
i = 0.3333333333x-1

Simplifying
i = 0.3333333333x-1
Subproblem 2
Set the factor '(5 + -8ix)' equal to zero and attempt to solve:

Simplifying
5 + -8ix = 0

Solving
5 + -8ix = 0

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

Add '-5' to each side of the equation.
5 + -5 + -8ix = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8ix = 0 + -5
-8ix = 0 + -5

Combine like terms: 0 + -5 = -5
-8ix = -5

Divide each side by '-8x'.
i = 0.625x-1

Simplifying
i = 0.625x-1
Solution
i = {0.3333333333x-1, 0.625x-1}