(14-2i)(7+12i)=

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Solution for (14-2i)(7+12i)= equation: 


Simplifying
(14 + -2i)(7 + 12i) = 0

Multiply (14 + -2i) * (7 + 12i)
(14(7 + 12i) + -2i * (7 + 12i)) = 0
((7 * 14 + 12i * 14) + -2i * (7 + 12i)) = 0
((98 + 168i) + -2i * (7 + 12i)) = 0
(98 + 168i + (7 * -2i + 12i * -2i)) = 0
(98 + 168i + (-14i + -24i2)) = 0

Combine like terms: 168i + -14i = 154i
(98 + 154i + -24i2) = 0

Solving
98 + 154i + -24i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(49 + 77i + -12i2) = 0

Factor a trinomial.
2((7 + -1i)(7 + 12i)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + -1i)' equal to zero and attempt to solve:

Simplifying
7 + -1i = 0

Solving
7 + -1i = 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 + -1i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1i = 0 + -7
-1i = 0 + -7

Combine like terms: 0 + -7 = -7
-1i = -7

Divide each side by '-1'.
i = 7

Simplifying
i = 7

Subproblem 2
Set the factor '(7 + 12i)' equal to zero and attempt to solve:

Simplifying
7 + 12i = 0

Solving
7 + 12i = 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 + 12i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 12i = 0 + -7
12i = 0 + -7

Combine like terms: 0 + -7 = -7
12i = -7

Divide each side by '12'.
i = -0.5833333333

Simplifying
i = -0.5833333333
Solution
i = {7, -0.5833333333}

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