(-6+12i)(-7-9i)=0

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Solution for (-6+12i)(-7-9i)=0 equation: 


Simplifying
(-6 + 12i)(-7 + -9i) = 0

Multiply (-6 + 12i) * (-7 + -9i)
(-6(-7 + -9i) + 12i * (-7 + -9i)) = 0
((-7 * -6 + -9i * -6) + 12i * (-7 + -9i)) = 0
((42 + 54i) + 12i * (-7 + -9i)) = 0
(42 + 54i + (-7 * 12i + -9i * 12i)) = 0
(42 + 54i + (-84i + -108i2)) = 0

Combine like terms: 54i + -84i = -30i
(42 + -30i + -108i2) = 0

Solving
42 + -30i + -108i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '6'.
6(7 + -5i + -18i2) = 0

Factor a trinomial.
6((1 + -2i)(7 + 9i)) = 0

Ignore the factor 6.

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

Simplifying
1 + -2i = 0

Solving
1 + -2i = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2i = 0 + -1
-2i = 0 + -1

Combine like terms: 0 + -1 = -1
-2i = -1

Divide each side by '-2'.
i = 0.5

Simplifying
i = 0.5

Subproblem 2
Set the factor '(7 + 9i)' equal to zero and attempt to solve:

Simplifying
7 + 9i = 0

Solving
7 + 9i = 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 + 9i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 9i = 0 + -7
9i = 0 + -7

Combine like terms: 0 + -7 = -7
9i = -7

Divide each side by '9'.
i = -0.7777777778

Simplifying
i = -0.7777777778
Solution
i = {0.5, -0.7777777778}

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