(8+2i)(3-7i)=

Solution for (8+2i)(3-7i)= equation:

Simplifying
(8 + 2i)(3 + -7i) = 0

Multiply (8 + 2i) * (3 + -7i)
(8(3 + -7i) + 2i * (3 + -7i)) = 0
((3 * 8 + -7i * 8) + 2i * (3 + -7i)) = 0
((24 + -56i) + 2i * (3 + -7i)) = 0
(24 + -56i + (3 * 2i + -7i * 2i)) = 0
(24 + -56i + (6i + -14i2)) = 0

Combine like terms: -56i + 6i = -50i
(24 + -50i + -14i2) = 0

Solving
24 + -50i + -14i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -25i + -7i2) = 0

Factor a trinomial.
2((3 + -7i)(4 + i)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -7i)' equal to zero and attempt to solve:

Simplifying
3 + -7i = 0

Solving
3 + -7i = 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 + -7i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7i = 0 + -3
-7i = 0 + -3

Combine like terms: 0 + -3 = -3
-7i = -3

Divide each side by '-7'.
i = 0.4285714286

Simplifying
i = 0.4285714286
Subproblem 2
Set the factor '(4 + i)' equal to zero and attempt to solve:

Simplifying
4 + i = 0

Solving
4 + i = 0

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

Add '-4' to each side of the equation.
4 + -4 + i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + i = 0 + -4
i = 0 + -4

Combine like terms: 0 + -4 = -4
i = -4

Simplifying
i = -4
Solution
i = {0.4285714286, -4}