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

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


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

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

Combine like terms: -9i + 7i = -2i
-1(21 + -2i + -3i2) = 0
(21 * -1 + -2i * -1 + -3i2 * -1) = 0
(-21 + 2i + 3i2) = 0

Solving
-21 + 2i + 3i2 = 0

Solving for variable 'i'.

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


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

Simplifying
-3 + -1i = 0

Solving
-3 + -1i = 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 + -1i = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1i = 0 + 3
-1i = 0 + 3

Combine like terms: 0 + 3 = 3
-1i = 3

Divide each side by '-1'.
i = -3

Simplifying
i = -3

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 = {-3, 2.333333333}

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