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

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


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

Reorder the terms:
(7 + 3i)(2i + -4) = 0

Reorder the terms:
(7 + 3i)(-4 + 2i) = 0

Multiply (7 + 3i) * (-4 + 2i)
(7(-4 + 2i) + 3i * (-4 + 2i)) = 0
((-4 * 7 + 2i * 7) + 3i * (-4 + 2i)) = 0
((-28 + 14i) + 3i * (-4 + 2i)) = 0
(-28 + 14i + (-4 * 3i + 2i * 3i)) = 0
(-28 + 14i + (-12i + 6i2)) = 0

Combine like terms: 14i + -12i = 2i
(-28 + 2i + 6i2) = 0

Solving
-28 + 2i + 6i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + i + 3i2) = 0

Factor a trinomial.
2((-7 + -3i)(2 + -1i)) = 0

Ignore the factor 2.

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 '(2 + -1i)' equal to zero and attempt to solve:

Simplifying
2 + -1i = 0

Solving
2 + -1i = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1i = 0 + -2
-1i = 0 + -2

Combine like terms: 0 + -2 = -2
-1i = -2

Divide each side by '-1'.
i = 2

Simplifying
i = 2
Solution
i = {-2.333333333, 2}

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