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

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

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

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

Combine like terms: 6i + 1i = 7i
(2 + 7i + 3i2) = 0

Solving
2 + 7i + 3i2 = 0

Solving for variable 'i'.

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

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

Simplifying
2 + i = 0

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

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

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

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

Simplifying
1 + 3i = 0

Solving
1 + 3i = 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 + 3i = 0 + -1

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

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

Divide each side by '3'.
i = -0.3333333333

Simplifying
i = -0.3333333333
Solution
i = {-2, -0.3333333333}