(-4+6i)(-5+3i)=

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Solution for (-4+6i)(-5+3i)= equation: 


Simplifying
(-4 + 6i)(-5 + 3i) = 0

Multiply (-4 + 6i) * (-5 + 3i)
(-4(-5 + 3i) + 6i * (-5 + 3i)) = 0
((-5 * -4 + 3i * -4) + 6i * (-5 + 3i)) = 0
((20 + -12i) + 6i * (-5 + 3i)) = 0
(20 + -12i + (-5 * 6i + 3i * 6i)) = 0
(20 + -12i + (-30i + 18i2)) = 0

Combine like terms: -12i + -30i = -42i
(20 + -42i + 18i2) = 0

Solving
20 + -42i + 18i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -21i + 9i2) = 0

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(5 + -3i)' equal to zero and attempt to solve:

Simplifying
5 + -3i = 0

Solving
5 + -3i = 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 + -3i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3i = 0 + -5
-3i = 0 + -5

Combine like terms: 0 + -5 = -5
-3i = -5

Divide each side by '-3'.
i = 1.666666667

Simplifying
i = 1.666666667
Solution
i = {0.6666666667, 1.666666667}

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