-1((7+3i)(5+3i))=0

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Solution for -1((7+3i)(5+3i))=0 equation: 


Simplifying
-1((7 + 3i)(5 + 3i)) = 0

Multiply (7 + 3i) * (5 + 3i)
-1((7(5 + 3i) + 3i * (5 + 3i))) = 0
-1(((5 * 7 + 3i * 7) + 3i * (5 + 3i))) = 0
-1(((35 + 21i) + 3i * (5 + 3i))) = 0
-1((35 + 21i + (5 * 3i + 3i * 3i))) = 0
-1((35 + 21i + (15i + 9i2))) = 0

Combine like terms: 21i + 15i = 36i
-1((35 + 36i + 9i2)) = 0
(35 * -1 + 36i * -1 + 9i2 * -1) = 0
(-35 + -36i + -9i2) = 0

Solving
-35 + -36i + -9i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(35 + 36i + 9i2) = 0

Factor a trinomial.
-1((7 + 3i)(5 + 3i)) = 0

Ignore the factor -1.

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 '(5 + 3i)' equal to zero and attempt to solve:

Simplifying
5 + 3i = 0

Solving
5 + 3i = 0

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

Add '-5' to each side of the equation.
5 + -5 + 3i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3i = 0 + -5
3i = 0 + -5

Combine like terms: 0 + -5 = -5
3i = -5

Divide each side by '3'.
i = -1.666666667

Simplifying
i = -1.666666667
Solution
i = {-2.333333333, -1.666666667}

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