(2+3i)(5-6i)=0

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Solution for (2+3i)(5-6i)=0 equation: 


Simplifying
(2 + 3i)(5 + -6i) = 0

Multiply (2 + 3i) * (5 + -6i)
(2(5 + -6i) + 3i * (5 + -6i)) = 0
((5 * 2 + -6i * 2) + 3i * (5 + -6i)) = 0
((10 + -12i) + 3i * (5 + -6i)) = 0
(10 + -12i + (5 * 3i + -6i * 3i)) = 0
(10 + -12i + (15i + -18i2)) = 0

Combine like terms: -12i + 15i = 3i
(10 + 3i + -18i2) = 0

Solving
10 + 3i + -18i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(5 + -6i)(2 + 3i) = 0


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 '(2 + 3i)' equal to zero and attempt to solve:

Simplifying
2 + 3i = 0

Solving
2 + 3i = 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 + 3i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3i = 0 + -2
3i = 0 + -2

Combine like terms: 0 + -2 = -2
3i = -2

Divide each side by '3'.
i = -0.6666666667

Simplifying
i = -0.6666666667
Solution
i = {0.8333333333, -0.6666666667}

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