(-3+8i)(1+5i)=0

Solution for (-3+8i)(1+5i)=0 equation:

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

Multiply (-3 + 8i) * (1 + 5i)
(-3(1 + 5i) + 8i * (1 + 5i)) = 0
((1 * -3 + 5i * -3) + 8i * (1 + 5i)) = 0
((-3 + -15i) + 8i * (1 + 5i)) = 0
(-3 + -15i + (1 * 8i + 5i * 8i)) = 0
(-3 + -15i + (8i + 40i2)) = 0

Combine like terms: -15i + 8i = -7i
(-3 + -7i + 40i2) = 0

Solving
-3 + -7i + 40i2 = 0

Solving for variable 'i'.

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

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

Simplifying
-1 + -5i = 0

Solving
-1 + -5i = 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 + -5i = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5i = 0 + 1
-5i = 0 + 1

Combine like terms: 0 + 1 = 1
-5i = 1

Divide each side by '-5'.
i = -0.2

Simplifying
i = -0.2
Subproblem 2
Set the factor '(3 + -8i)' equal to zero and attempt to solve:

Simplifying
3 + -8i = 0

Solving
3 + -8i = 0

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

Add '-3' to each side of the equation.
3 + -3 + -8i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8i = 0 + -3
-8i = 0 + -3

Combine like terms: 0 + -3 = -3
-8i = -3

Divide each side by '-8'.
i = 0.375

Simplifying
i = 0.375
Solution
i = {-0.2, 0.375}