(6-8i)(5+i)=0

Solution for (6-8i)(5+i)=0 equation:

Simplifying
(6 + -8i)(5 + i) = 0

Multiply (6 + -8i) * (5 + i)
(6(5 + i) + -8i * (5 + i)) = 0
((5 * 6 + i * 6) + -8i * (5 + i)) = 0
((30 + 6i) + -8i * (5 + i)) = 0
(30 + 6i + (5 * -8i + i * -8i)) = 0
(30 + 6i + (-40i + -8i2)) = 0

Combine like terms: 6i + -40i = -34i
(30 + -34i + -8i2) = 0

Solving
30 + -34i + -8i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -17i + -4i2) = 0

Factor a trinomial.
2((3 + -4i)(5 + i)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -4i)' equal to zero and attempt to solve:

Simplifying
3 + -4i = 0

Solving
3 + -4i = 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 + -4i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4i = 0 + -3
-4i = 0 + -3

Combine like terms: 0 + -3 = -3
-4i = -3

Divide each side by '-4'.
i = 0.75

Simplifying
i = 0.75
Subproblem 2
Set the factor '(5 + i)' equal to zero and attempt to solve:

Simplifying
5 + i = 0

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

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

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

Simplifying
i = -5
Solution
i = {0.75, -5}