(6-7i)*(3+8i)=

Solution for (6-7i)*(3+8i)= equation:

Simplifying
(6 + -7i)(3 + 8i) = 0

Multiply (6 + -7i) * (3 + 8i)
(6(3 + 8i) + -7i * (3 + 8i)) = 0
((3 * 6 + 8i * 6) + -7i * (3 + 8i)) = 0
((18 + 48i) + -7i * (3 + 8i)) = 0
(18 + 48i + (3 * -7i + 8i * -7i)) = 0
(18 + 48i + (-21i + -56i2)) = 0

Combine like terms: 48i + -21i = 27i
(18 + 27i + -56i2) = 0

Solving
18 + 27i + -56i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(6 + -7i)(3 + 8i) = 0

Subproblem 1
Set the factor '(6 + -7i)' equal to zero and attempt to solve:

Simplifying
6 + -7i = 0

Solving
6 + -7i = 0

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

Add '-6' to each side of the equation.
6 + -6 + -7i = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7i = 0 + -6
-7i = 0 + -6

Combine like terms: 0 + -6 = -6
-7i = -6

Divide each side by '-7'.
i = 0.8571428571

Simplifying
i = 0.8571428571
Subproblem 2
Set the factor '(3 + 8i)' equal to zero and attempt to solve:

Simplifying
3 + 8i = 0

Solving
3 + 8i = 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 + 8i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8i = 0 + -3
8i = 0 + -3

Combine like terms: 0 + -3 = -3
8i = -3

Divide each side by '8'.
i = -0.375

Simplifying
i = -0.375
Solution
i = {0.8571428571, -0.375}