(6+2i)(3-10i)=0

Solution for (6+2i)(3-10i)=0 equation:

Simplifying
(6 + 2i)(3 + -10i) = 0

Multiply (6 + 2i) * (3 + -10i)
(6(3 + -10i) + 2i * (3 + -10i)) = 0
((3 * 6 + -10i * 6) + 2i * (3 + -10i)) = 0
((18 + -60i) + 2i * (3 + -10i)) = 0
(18 + -60i + (3 * 2i + -10i * 2i)) = 0
(18 + -60i + (6i + -20i2)) = 0

Combine like terms: -60i + 6i = -54i
(18 + -54i + -20i2) = 0

Solving
18 + -54i + -20i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -27i + -10i2) = 0

Factor a trinomial.
2((3 + -10i)(3 + i)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -10i)' equal to zero and attempt to solve:

Simplifying
3 + -10i = 0

Solving
3 + -10i = 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 + -10i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -10i = 0 + -3
-10i = 0 + -3

Combine like terms: 0 + -3 = -3
-10i = -3

Divide each side by '-10'.
i = 0.3

Simplifying
i = 0.3
Subproblem 2
Set the factor '(3 + i)' equal to zero and attempt to solve:

Simplifying
3 + i = 0

Solving
3 + i = 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 + i = 0 + -3

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

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

Simplifying
i = -3
Solution
i = {0.3, -3}