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

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

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

Multiply (-6 + 2i) * (7 + i)
(-6(7 + i) + 2i * (7 + i)) = 0
((7 * -6 + i * -6) + 2i * (7 + i)) = 0
((-42 + -6i) + 2i * (7 + i)) = 0
(-42 + -6i + (7 * 2i + i * 2i)) = 0
(-42 + -6i + (14i + 2i2)) = 0

Combine like terms: -6i + 14i = 8i
(-42 + 8i + 2i2) = 0

Solving
-42 + 8i + 2i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 4i + i2) = 0

Factor a trinomial.
2((-7 + -1i)(3 + -1i)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -1i)' equal to zero and attempt to solve:

Simplifying
-7 + -1i = 0

Solving
-7 + -1i = 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 + -1i = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1i = 0 + 7
-1i = 0 + 7

Combine like terms: 0 + 7 = 7
-1i = 7

Divide each side by '-1'.
i = -7

Simplifying
i = -7
Subproblem 2
Set the factor '(3 + -1i)' equal to zero and attempt to solve:

Simplifying
3 + -1i = 0

Solving
3 + -1i = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1i = 0 + -3
-1i = 0 + -3

Combine like terms: 0 + -3 = -3
-1i = -3

Divide each side by '-1'.
i = 3

Simplifying
i = 3
Solution
i = {-7, 3}