(5-3i)(2+i)=10-3i

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Solution for (5-3i)(2+i)=10-3i equation: 


Simplifying
(5 + -3i)(2 + i) = 10 + -3i

Multiply (5 + -3i) * (2 + i)
(5(2 + i) + -3i * (2 + i)) = 10 + -3i
((2 * 5 + i * 5) + -3i * (2 + i)) = 10 + -3i
((10 + 5i) + -3i * (2 + i)) = 10 + -3i
(10 + 5i + (2 * -3i + i * -3i)) = 10 + -3i
(10 + 5i + (-6i + -3i2)) = 10 + -3i

Combine like terms: 5i + -6i = -1i
(10 + -1i + -3i2) = 10 + -3i

Add '-10' to each side of the equation.
10 + -1i + -10 + -3i2 = 10 + -10 + -3i

Reorder the terms:
10 + -10 + -1i + -3i2 = 10 + -10 + -3i

Combine like terms: 10 + -10 = 0
0 + -1i + -3i2 = 10 + -10 + -3i
-1i + -3i2 = 10 + -10 + -3i

Combine like terms: 10 + -10 = 0
-1i + -3i2 = 0 + -3i
-1i + -3i2 = -3i

Solving
-1i + -3i2 = -3i

Solving for variable 'i'.

Reorder the terms:
-1i + 3i + -3i2 = -3i + 3i

Combine like terms: -1i + 3i = 2i
2i + -3i2 = -3i + 3i

Combine like terms: -3i + 3i = 0
2i + -3i2 = 0

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


Subproblem 1
Set the factor 'i' equal to zero and attempt to solve:

Simplifying
i = 0

Solving
i = 0

Move all terms containing i to the left, all other terms to the right.

Simplifying
i = 0

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, 0.6666666667}

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