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

Solution for (3+7i)(-2-2i)=0 equation:

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

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

Combine like terms: -6i + -14i = -20i
(-6 + -20i + -14i2) = 0

Solving
-6 + -20i + -14i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(3 + 10i + 7i2) = 0

Factor a trinomial.
-2((1 + i)(3 + 7i)) = 0

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

Simplifying
1 + i = 0

Solving
1 + i = 0

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

Add '-1' to each side of the equation.
1 + -1 + i = 0 + -1

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

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

Simplifying
i = -1
Subproblem 2
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
Solution
i = {-1, -0.4285714286}