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

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


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

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

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

Multiply (7i + 3x) * (-4i + 7x)
(7i * (-4i + 7x) + 3x * (-4i + 7x)) = 0
((-4i * 7i + 7x * 7i) + 3x * (-4i + 7x)) = 0

Reorder the terms:
((49ix + -28i2) + 3x * (-4i + 7x)) = 0
((49ix + -28i2) + 3x * (-4i + 7x)) = 0
(49ix + -28i2 + (-4i * 3x + 7x * 3x)) = 0
(49ix + -28i2 + (-12ix + 21x2)) = 0

Reorder the terms:
(49ix + -12ix + -28i2 + 21x2) = 0

Combine like terms: 49ix + -12ix = 37ix
(37ix + -28i2 + 21x2) = 0

Solving
37ix + -28i2 + 21x2 = 0

Solving for variable 'i'.

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


Subproblem 1
Set the factor '(-7i + -3x)' equal to zero and attempt to solve:

Simplifying
-7i + -3x = 0

Solving
-7i + -3x = 0

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

Add '3x' to each side of the equation.
-7i + -3x + 3x = 0 + 3x

Combine like terms: -3x + 3x = 0
-7i + 0 = 0 + 3x
-7i = 0 + 3x
Remove the zero:
-7i = 3x

Divide each side by '-7'.
i = -0.4285714286x

Simplifying
i = -0.4285714286x

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

Simplifying
4i + -7x = 0

Solving
4i + -7x = 0

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

Add '7x' to each side of the equation.
4i + -7x + 7x = 0 + 7x

Combine like terms: -7x + 7x = 0
4i + 0 = 0 + 7x
4i = 0 + 7x
Remove the zero:
4i = 7x

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

Simplifying
i = 1.75x
Solution
i = {-0.4285714286x, 1.75x}

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