(-5-2i)(6+7i)=

Solution for (-5-2i)(6+7i)= equation:

Simplifying
(-5 + -2i)(6 + 7i) = 0

Multiply (-5 + -2i) * (6 + 7i)
(-5(6 + 7i) + -2i * (6 + 7i)) = 0
((6 * -5 + 7i * -5) + -2i * (6 + 7i)) = 0
((-30 + -35i) + -2i * (6 + 7i)) = 0
(-30 + -35i + (6 * -2i + 7i * -2i)) = 0
(-30 + -35i + (-12i + -14i2)) = 0

Combine like terms: -35i + -12i = -47i
(-30 + -47i + -14i2) = 0

Solving
-30 + -47i + -14i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(30 + 47i + 14i2) = 0

Factor a trinomial.
-1((5 + 2i)(6 + 7i)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + 2i)' equal to zero and attempt to solve:

Simplifying
5 + 2i = 0

Solving
5 + 2i = 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 + 2i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2i = 0 + -5
2i = 0 + -5

Combine like terms: 0 + -5 = -5
2i = -5

Divide each side by '2'.
i = -2.5

Simplifying
i = -2.5
Subproblem 2
Set the factor '(6 + 7i)' equal to zero and attempt to solve:

Simplifying
6 + 7i = 0

Solving
6 + 7i = 0

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

Add '-6' to each side of the equation.
6 + -6 + 7i = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 7i = 0 + -6
7i = 0 + -6

Combine like terms: 0 + -6 = -6
7i = -6

Divide each side by '7'.
i = -0.8571428571

Simplifying
i = -0.8571428571
Solution
i = {-2.5, -0.8571428571}