(-9+7i)(3+i)=

Solution for (-9+7i)(3+i)= equation:

Simplifying
(-9 + 7i)(3 + i) = 0

Multiply (-9 + 7i) * (3 + i)
(-9(3 + i) + 7i * (3 + i)) = 0
((3 * -9 + i * -9) + 7i * (3 + i)) = 0
((-27 + -9i) + 7i * (3 + i)) = 0
(-27 + -9i + (3 * 7i + i * 7i)) = 0
(-27 + -9i + (21i + 7i2)) = 0

Combine like terms: -9i + 21i = 12i
(-27 + 12i + 7i2) = 0

Solving
-27 + 12i + 7i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-3 + -1i)(9 + -7i) = 0

Subproblem 1
Set the factor '(-3 + -1i)' equal to zero and attempt to solve:

Simplifying
-3 + -1i = 0

Solving
-3 + -1i = 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 + -1i = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1i = 0 + 3
-1i = 0 + 3

Combine like terms: 0 + 3 = 3
-1i = 3

Divide each side by '-1'.
i = -3

Simplifying
i = -3
Subproblem 2
Set the factor '(9 + -7i)' equal to zero and attempt to solve:

Simplifying
9 + -7i = 0

Solving
9 + -7i = 0

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

Add '-9' to each side of the equation.
9 + -9 + -7i = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -7i = 0 + -9
-7i = 0 + -9

Combine like terms: 0 + -9 = -9
-7i = -9

Divide each side by '-7'.
i = 1.285714286

Simplifying
i = 1.285714286
Solution
i = {-3, 1.285714286}