(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 + -1i + -3i2) = 0

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
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
Solution
i = {1.666666667, -2}

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