(3-4i)(7+2i)=0

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Solution for (3-4i)(7+2i)=0 equation: 


Simplifying
(3 + -4i)(7 + 2i) = 0

Multiply (3 + -4i) * (7 + 2i)
(3(7 + 2i) + -4i * (7 + 2i)) = 0
((7 * 3 + 2i * 3) + -4i * (7 + 2i)) = 0
((21 + 6i) + -4i * (7 + 2i)) = 0
(21 + 6i + (7 * -4i + 2i * -4i)) = 0
(21 + 6i + (-28i + -8i2)) = 0

Combine like terms: 6i + -28i = -22i
(21 + -22i + -8i2) = 0

Solving
21 + -22i + -8i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(3 + -4i)(7 + 2i) = 0


Subproblem 1
Set the factor '(3 + -4i)' equal to zero and attempt to solve:

Simplifying
3 + -4i = 0

Solving
3 + -4i = 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 + -4i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4i = 0 + -3
-4i = 0 + -3

Combine like terms: 0 + -3 = -3
-4i = -3

Divide each side by '-4'.
i = 0.75

Simplifying
i = 0.75

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

Simplifying
7 + 2i = 0

Solving
7 + 2i = 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 + 2i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2i = 0 + -7
2i = 0 + -7

Combine like terms: 0 + -7 = -7
2i = -7

Divide each side by '2'.
i = -3.5

Simplifying
i = -3.5
Solution
i = {0.75, -3.5}

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