(3-4i)(2+i)=

Solution for (3-4i)(2+i)= equation:

Simplifying
(3 + -4i)(2 + i) = 0

Multiply (3 + -4i) * (2 + i)
(3(2 + i) + -4i * (2 + i)) = 0
((2 * 3 + i * 3) + -4i * (2 + i)) = 0
((6 + 3i) + -4i * (2 + i)) = 0
(6 + 3i + (2 * -4i + i * -4i)) = 0
(6 + 3i + (-8i + -4i2)) = 0

Combine like terms: 3i + -8i = -5i
(6 + -5i + -4i2) = 0

Solving
6 + -5i + -4i2 = 0

Solving for variable 'i'.

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

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 '(2 + i)' equal to zero and attempt to solve:

Simplifying
2 + i = 0

Solving
2 + i = 0

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

Add '-2' to each side of the equation.
2 + -2 + i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + i = 0 + -2
i = 0 + -2

Combine like terms: 0 + -2 = -2
i = -2

Simplifying
i = -2
Solution
i = {0.75, -2}