(6+7i)(6+i)=

Solution for (6+7i)(6+i)= equation:

Simplifying
(6 + 7i)(6 + i) = 0

Multiply (6 + 7i) * (6 + i)
(6(6 + i) + 7i * (6 + i)) = 0
((6 * 6 + i * 6) + 7i * (6 + i)) = 0
((36 + 6i) + 7i * (6 + i)) = 0
(36 + 6i + (6 * 7i + i * 7i)) = 0
(36 + 6i + (42i + 7i2)) = 0

Combine like terms: 6i + 42i = 48i
(36 + 48i + 7i2) = 0

Solving
36 + 48i + 7i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(6 + i)(6 + 7i) = 0

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 '(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 = {-6, -0.8571428571}