(-3+9i)(4+i)=

Solution for (-3+9i)(4+i)= equation:

Simplifying
(-3 + 9i)(4 + i) = 0

Multiply (-3 + 9i) * (4 + i)
(-3(4 + i) + 9i * (4 + i)) = 0
((4 * -3 + i * -3) + 9i * (4 + i)) = 0
((-12 + -3i) + 9i * (4 + i)) = 0
(-12 + -3i + (4 * 9i + i * 9i)) = 0
(-12 + -3i + (36i + 9i2)) = 0

Combine like terms: -3i + 36i = 33i
(-12 + 33i + 9i2) = 0

Solving
-12 + 33i + 9i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 11i + 3i2) = 0

Factor a trinomial.
3((-4 + -1i)(1 + -3i)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -1i)' equal to zero and attempt to solve:

Simplifying
-4 + -1i = 0

Solving
-4 + -1i = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1i = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1i = 0 + 4
-1i = 0 + 4

Combine like terms: 0 + 4 = 4
-1i = 4

Divide each side by '-1'.
i = -4

Simplifying
i = -4
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 = {-4, 0.3333333333}