(1+5i)(6-3i)=0

Solution for (1+5i)(6-3i)=0 equation:

Simplifying
(1 + 5i)(6 + -3i) = 0

Multiply (1 + 5i) * (6 + -3i)
(1(6 + -3i) + 5i * (6 + -3i)) = 0
((6 * 1 + -3i * 1) + 5i * (6 + -3i)) = 0
((6 + -3i) + 5i * (6 + -3i)) = 0
(6 + -3i + (6 * 5i + -3i * 5i)) = 0
(6 + -3i + (30i + -15i2)) = 0

Combine like terms: -3i + 30i = 27i
(6 + 27i + -15i2) = 0

Solving
6 + 27i + -15i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 9i + -5i2) = 0

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

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

Simplifying
2 + -1i = 0

Solving
2 + -1i = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1i = 0 + -2

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

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

Divide each side by '-1'.
i = 2

Simplifying
i = 2
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 = {2, -0.2}