(7+2i)(9-6i)=

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Solution for (7+2i)(9-6i)= equation: 


Simplifying
(7 + 2i)(9 + -6i) = 0

Multiply (7 + 2i) * (9 + -6i)
(7(9 + -6i) + 2i * (9 + -6i)) = 0
((9 * 7 + -6i * 7) + 2i * (9 + -6i)) = 0
((63 + -42i) + 2i * (9 + -6i)) = 0
(63 + -42i + (9 * 2i + -6i * 2i)) = 0
(63 + -42i + (18i + -12i2)) = 0

Combine like terms: -42i + 18i = -24i
(63 + -24i + -12i2) = 0

Solving
63 + -24i + -12i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(21 + -8i + -4i2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(3 + -2i)' equal to zero and attempt to solve:

Simplifying
3 + -2i = 0

Solving
3 + -2i = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2i = 0 + -3

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

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

Divide each side by '-2'.
i = 1.5

Simplifying
i = 1.5

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 = {1.5, -3.5}

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