(i-3)(3i+3)=

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

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

Reorder the terms:
(-3 + i)(3i + 3) = 0

Reorder the terms:
(-3 + i)(3 + 3i) = 0

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

Combine like terms: -9i + 3i = -6i
(-9 + -6i + 3i2) = 0

Solving
-9 + -6i + 3i2 = 0

Solving for variable 'i'.

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

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

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

Simplifying
-1 + -1i = 0

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

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

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

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

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

Simplifying
3 + -1i = 0

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

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

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

Divide each side by '-1'.
i = 3

Simplifying
i = 3
Solution
i = {-1, 3}