(3+5i)(6-7i)=

Solution for (3+5i)(6-7i)= equation:

Simplifying
(3 + 5i)(6 + -7i) = 0

Multiply (3 + 5i) * (6 + -7i)
(3(6 + -7i) + 5i * (6 + -7i)) = 0
((6 * 3 + -7i * 3) + 5i * (6 + -7i)) = 0
((18 + -21i) + 5i * (6 + -7i)) = 0
(18 + -21i + (6 * 5i + -7i * 5i)) = 0
(18 + -21i + (30i + -35i2)) = 0

Combine like terms: -21i + 30i = 9i
(18 + 9i + -35i2) = 0

Solving
18 + 9i + -35i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(6 + -7i)(3 + 5i) = 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 + 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 = {0.8571428571, -0.6}