(7-3i)(4-6i)=

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Solution for (7-3i)(4-6i)= equation: 


Simplifying
(7 + -3i)(4 + -6i) = 0

Multiply (7 + -3i) * (4 + -6i)
(7(4 + -6i) + -3i * (4 + -6i)) = 0
((4 * 7 + -6i * 7) + -3i * (4 + -6i)) = 0
((28 + -42i) + -3i * (4 + -6i)) = 0
(28 + -42i + (4 * -3i + -6i * -3i)) = 0
(28 + -42i + (-12i + 18i2)) = 0

Combine like terms: -42i + -12i = -54i
(28 + -54i + 18i2) = 0

Solving
28 + -54i + 18i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + -27i + 9i2) = 0

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(7 + -3i)' equal to zero and attempt to solve:

Simplifying
7 + -3i = 0

Solving
7 + -3i = 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 + -3i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3i = 0 + -7
-3i = 0 + -7

Combine like terms: 0 + -7 = -7
-3i = -7

Divide each side by '-3'.
i = 2.333333333

Simplifying
i = 2.333333333
Solution
i = {0.6666666667, 2.333333333}

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