(-1+2i)(3+10i)=0

Solution for (-1+2i)(3+10i)=0 equation:

Simplifying
(-1 + 2i)(3 + 10i) = 0

Multiply (-1 + 2i) * (3 + 10i)
(-1(3 + 10i) + 2i * (3 + 10i)) = 0
((3 * -1 + 10i * -1) + 2i * (3 + 10i)) = 0
((-3 + -10i) + 2i * (3 + 10i)) = 0
(-3 + -10i + (3 * 2i + 10i * 2i)) = 0
(-3 + -10i + (6i + 20i2)) = 0

Combine like terms: -10i + 6i = -4i
(-3 + -4i + 20i2) = 0

Solving
-3 + -4i + 20i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-3 + -10i)(1 + -2i) = 0

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 '(1 + -2i)' equal to zero and attempt to solve:

Simplifying
1 + -2i = 0

Solving
1 + -2i = 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 + -2i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2i = 0 + -1
-2i = 0 + -1

Combine like terms: 0 + -1 = -1
-2i = -1

Divide each side by '-2'.
i = 0.5

Simplifying
i = 0.5
Solution
i = {-0.3, 0.5}