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

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


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

Multiply (6 + 3i) * (-7 + -3i)
(6(-7 + -3i) + 3i * (-7 + -3i)) = 0
((-7 * 6 + -3i * 6) + 3i * (-7 + -3i)) = 0
((-42 + -18i) + 3i * (-7 + -3i)) = 0
(-42 + -18i + (-7 * 3i + -3i * 3i)) = 0
(-42 + -18i + (-21i + -9i2)) = 0

Combine like terms: -18i + -21i = -39i
(-42 + -39i + -9i2) = 0

Solving
-42 + -39i + -9i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-3'.
-3(14 + 13i + 3i2) = 0

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

Ignore the factor -3.

Subproblem 1
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

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 = {-2.333333333, -2}

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