(6+2i)(-1+5i)=0

Solution for (6+2i)(-1+5i)=0 equation:

Simplifying
(6 + 2i)(-1 + 5i) = 0

Multiply (6 + 2i) * (-1 + 5i)
(6(-1 + 5i) + 2i * (-1 + 5i)) = 0
((-1 * 6 + 5i * 6) + 2i * (-1 + 5i)) = 0
((-6 + 30i) + 2i * (-1 + 5i)) = 0
(-6 + 30i + (-1 * 2i + 5i * 2i)) = 0
(-6 + 30i + (-2i + 10i2)) = 0

Combine like terms: 30i + -2i = 28i
(-6 + 28i + 10i2) = 0

Solving
-6 + 28i + 10i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 14i + 5i2) = 0

Factor a trinomial.
2((-3 + -1i)(1 + -5i)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + -5i)' equal to zero and attempt to solve:

Simplifying
1 + -5i = 0

Solving
1 + -5i = 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 + -5i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5i = 0 + -1
-5i = 0 + -1

Combine like terms: 0 + -1 = -1
-5i = -1

Divide each side by '-5'.
i = 0.2

Simplifying
i = 0.2
Solution
i = {-3, 0.2}