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

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

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

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

Combine like terms: -3i + -14i = -17i
(-6 + -17i + -7i2) = 0

Solving
-6 + -17i + -7i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 17i + 7i2) = 0

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

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

Simplifying
2 + i = 0

Solving
2 + i = 0

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

Add '-2' to each side of the equation.
2 + -2 + i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + i = 0 + -2
i = 0 + -2

Combine like terms: 0 + -2 = -2
i = -2

Simplifying
i = -2
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 = {-2, -0.4285714286}