(6+i)(1+i)=

Solution for (6+i)(1+i)= equation:

Simplifying
(6 + i)(1 + i) = 0

Multiply (6 + i) * (1 + i)
(6(1 + i) + i(1 + i)) = 0
((1 * 6 + i * 6) + i(1 + i)) = 0
((6 + 6i) + i(1 + i)) = 0
(6 + 6i + (1 * i + i * i)) = 0
(6 + 6i + (1i + i2)) = 0

Combine like terms: 6i + 1i = 7i
(6 + 7i + i2) = 0

Solving
6 + 7i + i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(6 + i)(1 + i) = 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 '(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}