(-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.
(-2 + -1i)(3 + -4i) = 0

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

Simplifying
-2 + -1i = 0

Solving
-2 + -1i = 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 + -1i = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1i = 0 + 2
-1i = 0 + 2

Combine like terms: 0 + 2 = 2
-1i = 2

Divide each side by '-1'.
i = -2

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