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

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

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

Multiply (6 + 7i) * (7 + i)
(6(7 + i) + 7i * (7 + i)) = 0
((7 * 6 + i * 6) + 7i * (7 + i)) = 0
((42 + 6i) + 7i * (7 + i)) = 0
(42 + 6i + (7 * 7i + i * 7i)) = 0
(42 + 6i + (49i + 7i2)) = 0

Combine like terms: 6i + 49i = 55i
(42 + 55i + 7i2) = 0

Solving
42 + 55i + 7i2 = 0

Solving for variable 'i'.

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

Subproblem 1
Set the factor '(7 + i)' equal to zero and attempt to solve:

Simplifying
7 + i = 0

Solving
7 + i = 0

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

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

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

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

Simplifying
i = -7
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 = {-7, -0.8571428571}