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

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Solution for (4-2i)(5+3i)=0 equation: 


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

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

Combine like terms: 12i + -10i = 2i
(20 + 2i + -6i2) = 0

Solving
20 + 2i + -6i2 = 0

Solving for variable 'i'.

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

Factor a trinomial.
2((2 + -1i)(5 + 3i)) = 0

Ignore the factor 2.

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

Simplifying
2 + -1i = 0

Solving
2 + -1i = 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 + -1i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1i = 0 + -2
-1i = 0 + -2

Combine like terms: 0 + -2 = -2
-1i = -2

Divide each side by '-1'.
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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