(3-4i)(5+7i)=

Solution for (3-4i)(5+7i)= equation:

Simplifying
(3 + -4i)(5 + 7i) = 0

Multiply (3 + -4i) * (5 + 7i)
(3(5 + 7i) + -4i * (5 + 7i)) = 0
((5 * 3 + 7i * 3) + -4i * (5 + 7i)) = 0
((15 + 21i) + -4i * (5 + 7i)) = 0
(15 + 21i + (5 * -4i + 7i * -4i)) = 0
(15 + 21i + (-20i + -28i2)) = 0

Combine like terms: 21i + -20i = 1i
(15 + 1i + -28i2) = 0

Solving
15 + 1i + -28i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(3 + -4i)(5 + 7i) = 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 '(5 + 7i)' equal to zero and attempt to solve:

Simplifying
5 + 7i = 0

Solving
5 + 7i = 0

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

Add '-5' to each side of the equation.
5 + -5 + 7i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 7i = 0 + -5
7i = 0 + -5

Combine like terms: 0 + -5 = -5
7i = -5

Divide each side by '7'.
i = -0.7142857143

Simplifying
i = -0.7142857143
Solution
i = {0.75, -0.7142857143}