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

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

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

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

Combine like terms: -2i + -3i = -5i
(-6 + -5i + -1i2) = 0

Solving
-6 + -5i + -1i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 5i + i2) = 0

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

Ignore the factor -1.
Subproblem 1
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
Subproblem 2
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
Solution
i = {-3, -2}