(3+3i)(-7+4i)=0

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Solution for (3+3i)(-7+4i)=0 equation: 


Simplifying
(3 + 3i)(-7 + 4i) = 0

Multiply (3 + 3i) * (-7 + 4i)
(3(-7 + 4i) + 3i * (-7 + 4i)) = 0
((-7 * 3 + 4i * 3) + 3i * (-7 + 4i)) = 0
((-21 + 12i) + 3i * (-7 + 4i)) = 0
(-21 + 12i + (-7 * 3i + 4i * 3i)) = 0
(-21 + 12i + (-21i + 12i2)) = 0

Combine like terms: 12i + -21i = -9i
(-21 + -9i + 12i2) = 0

Solving
-21 + -9i + 12i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + -3i + 4i2) = 0

Factor a trinomial.
3((-1 + -1i)(7 + -4i)) = 0

Ignore the factor 3.

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

Simplifying
-1 + -1i = 0

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

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

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

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

Simplifying
i = -1

Subproblem 2
Set the factor '(7 + -4i)' equal to zero and attempt to solve:

Simplifying
7 + -4i = 0

Solving
7 + -4i = 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 + -4i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4i = 0 + -7
-4i = 0 + -7

Combine like terms: 0 + -7 = -7
-4i = -7

Divide each side by '-4'.
i = 1.75

Simplifying
i = 1.75
Solution
i = {-1, 1.75}

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