(5+5i)(6+i)=

Solution for (5+5i)(6+i)= equation:

Simplifying
(5 + 5i)(6 + i) = 0

Multiply (5 + 5i) * (6 + i)
(5(6 + i) + 5i * (6 + i)) = 0
((6 * 5 + i * 5) + 5i * (6 + i)) = 0
((30 + 5i) + 5i * (6 + i)) = 0
(30 + 5i + (6 * 5i + i * 5i)) = 0
(30 + 5i + (30i + 5i2)) = 0

Combine like terms: 5i + 30i = 35i
(30 + 35i + 5i2) = 0

Solving
30 + 35i + 5i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '5'.
5(6 + 7i + i2) = 0

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

Ignore the factor 5.
Subproblem 1
Set the factor '(6 + i)' equal to zero and attempt to solve:

Simplifying
6 + i = 0

Solving
6 + i = 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 + i = 0 + -6

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

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

Simplifying
i = -6
Subproblem 2
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
Solution
i = {-6, -1}