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

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


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

Multiply (5 + 6i) * (3 + -3i)
0 = (5(3 + -3i) + 6i * (3 + -3i))
0 = ((3 * 5 + -3i * 5) + 6i * (3 + -3i))
0 = ((15 + -15i) + 6i * (3 + -3i))
0 = (15 + -15i + (3 * 6i + -3i * 6i))
0 = (15 + -15i + (18i + -18i2))

Combine like terms: -15i + 18i = 3i
0 = (15 + 3i + -18i2)

Solving
0 = 15 + 3i + -18i2

Solving for variable 'i'.

Combine like terms: 0 + -15 = -15
-15 + -3i + 18i2 = 15 + 3i + -18i2 + -15 + -3i + 18i2

Reorder the terms:
-15 + -3i + 18i2 = 15 + -15 + 3i + -3i + -18i2 + 18i2

Combine like terms: 15 + -15 = 0
-15 + -3i + 18i2 = 0 + 3i + -3i + -18i2 + 18i2
-15 + -3i + 18i2 = 3i + -3i + -18i2 + 18i2

Combine like terms: 3i + -3i = 0
-15 + -3i + 18i2 = 0 + -18i2 + 18i2
-15 + -3i + 18i2 = -18i2 + 18i2

Combine like terms: -18i2 + 18i2 = 0
-15 + -3i + 18i2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -1i + 6i2) = 0

Factor a trinomial.
3((-5 + -6i)(1 + -1i)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-5 + -6i)' equal to zero and attempt to solve:

Simplifying
-5 + -6i = 0

Solving
-5 + -6i = 0

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

Add '5' to each side of the equation.
-5 + 5 + -6i = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6i = 0 + 5
-6i = 0 + 5

Combine like terms: 0 + 5 = 5
-6i = 5

Divide each side by '-6'.
i = -0.8333333333

Simplifying
i = -0.8333333333

Subproblem 2
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
Solution
i = {-0.8333333333, 1}

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