(6-3i)(7-2i)=

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Solution for (6-3i)(7-2i)= equation: 


Simplifying
(6 + -3i)(7 + -2i) = 0

Multiply (6 + -3i) * (7 + -2i)
(6(7 + -2i) + -3i * (7 + -2i)) = 0
((7 * 6 + -2i * 6) + -3i * (7 + -2i)) = 0
((42 + -12i) + -3i * (7 + -2i)) = 0
(42 + -12i + (7 * -3i + -2i * -3i)) = 0
(42 + -12i + (-21i + 6i2)) = 0

Combine like terms: -12i + -21i = -33i
(42 + -33i + 6i2) = 0

Solving
42 + -33i + 6i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(14 + -11i + 2i2) = 0

Factor a trinomial.
3((2 + -1i)(7 + -2i)) = 0

Ignore the factor 3.

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 '(7 + -2i)' equal to zero and attempt to solve:

Simplifying
7 + -2i = 0

Solving
7 + -2i = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2i = 0 + -7
-2i = 0 + -7

Combine like terms: 0 + -7 = -7
-2i = -7

Divide each side by '-2'.
i = 3.5

Simplifying
i = 3.5
Solution
i = {2, 3.5}

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