(3-5i)(-6+8i)=

Solution for (3-5i)(-6+8i)= equation:

Simplifying
(3 + -5i)(-6 + 8i) = 0

Multiply (3 + -5i) * (-6 + 8i)
(3(-6 + 8i) + -5i * (-6 + 8i)) = 0
((-6 * 3 + 8i * 3) + -5i * (-6 + 8i)) = 0
((-18 + 24i) + -5i * (-6 + 8i)) = 0
(-18 + 24i + (-6 * -5i + 8i * -5i)) = 0
(-18 + 24i + (30i + -40i2)) = 0

Combine like terms: 24i + 30i = 54i
(-18 + 54i + -40i2) = 0

Solving
-18 + 54i + -40i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 27i + -20i2) = 0

Factor a trinomial.
2((-3 + 4i)(3 + -5i)) = 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 '(3 + -5i)' equal to zero and attempt to solve:

Simplifying
3 + -5i = 0

Solving
3 + -5i = 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 + -5i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5i = 0 + -3
-5i = 0 + -3

Combine like terms: 0 + -3 = -3
-5i = -3

Divide each side by '-5'.
i = 0.6

Simplifying
i = 0.6
Solution
i = {0.75, 0.6}