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

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

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

Multiply (4 + 2i) * (3 + -4i)
(4(3 + -4i) + 2i * (3 + -4i)) = 0
((3 * 4 + -4i * 4) + 2i * (3 + -4i)) = 0
((12 + -16i) + 2i * (3 + -4i)) = 0
(12 + -16i + (3 * 2i + -4i * 2i)) = 0
(12 + -16i + (6i + -8i2)) = 0

Combine like terms: -16i + 6i = -10i
(12 + -10i + -8i2) = 0

Solving
12 + -10i + -8i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -5i + -4i2) = 0

Factor a trinomial.
2((3 + -4i)(2 + 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 '(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}