(4x-3i)(6x+2i)=

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Solution for (4x-3i)(6x+2i)= equation: 


Simplifying
(4x + -3i)(6x + 2i) = 0

Reorder the terms:
(-3i + 4x)(6x + 2i) = 0

Reorder the terms:
(-3i + 4x)(2i + 6x) = 0

Multiply (-3i + 4x) * (2i + 6x)
(-3i * (2i + 6x) + 4x * (2i + 6x)) = 0
((2i * -3i + 6x * -3i) + 4x * (2i + 6x)) = 0

Reorder the terms:
((-18ix + -6i2) + 4x * (2i + 6x)) = 0
((-18ix + -6i2) + 4x * (2i + 6x)) = 0
(-18ix + -6i2 + (2i * 4x + 6x * 4x)) = 0
(-18ix + -6i2 + (8ix + 24x2)) = 0

Reorder the terms:
(-18ix + 8ix + -6i2 + 24x2) = 0

Combine like terms: -18ix + 8ix = -10ix
(-10ix + -6i2 + 24x2) = 0

Solving
-10ix + -6i2 + 24x2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5ix + -3i2 + 12x2) = 0

Factor a trinomial.
2((-1i + -3x)(3i + -4x)) = 0

Ignore the factor 2.

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

Simplifying
-1i + -3x = 0

Solving
-1i + -3x = 0

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

Add '3x' to each side of the equation.
-1i + -3x + 3x = 0 + 3x

Combine like terms: -3x + 3x = 0
-1i + 0 = 0 + 3x
-1i = 0 + 3x
Remove the zero:
-1i = 3x

Divide each side by '-1'.
i = -3x

Simplifying
i = -3x

Subproblem 2
Set the factor '(3i + -4x)' equal to zero and attempt to solve:

Simplifying
3i + -4x = 0

Solving
3i + -4x = 0

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

Add '4x' to each side of the equation.
3i + -4x + 4x = 0 + 4x

Combine like terms: -4x + 4x = 0
3i + 0 = 0 + 4x
3i = 0 + 4x
Remove the zero:
3i = 4x

Divide each side by '3'.
i = 1.333333333x

Simplifying
i = 1.333333333x
Solution
i = {-3x, 1.333333333x}

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