(5-3i)(-4+2i)=

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Solution for (5-3i)(-4+2i)= equation: 


Simplifying
(5 + -3i)(-4 + 2i) = 0

Multiply (5 + -3i) * (-4 + 2i)
(5(-4 + 2i) + -3i * (-4 + 2i)) = 0
((-4 * 5 + 2i * 5) + -3i * (-4 + 2i)) = 0
((-20 + 10i) + -3i * (-4 + 2i)) = 0
(-20 + 10i + (-4 * -3i + 2i * -3i)) = 0
(-20 + 10i + (12i + -6i2)) = 0

Combine like terms: 10i + 12i = 22i
(-20 + 22i + -6i2) = 0

Solving
-20 + 22i + -6i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 11i + -3i2) = 0

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

Ignore the factor 2.

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

Simplifying
-2 + i = 0

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

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

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

Simplifying
i = 2

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 = {2, 1.666666667}

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