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Simplifying
(6x + -3i)(4x + 2i) = 0
Reorder the terms:
(-3i + 6x)(4x + 2i) = 0
Reorder the terms:
(-3i + 6x)(2i + 4x) = 0
Multiply (-3i + 6x) * (2i + 4x)
(-3i * (2i + 4x) + 6x * (2i + 4x)) = 0
((2i * -3i + 4x * -3i) + 6x * (2i + 4x)) = 0
Reorder the terms:
((-12ix + -6i2) + 6x * (2i + 4x)) = 0
((-12ix + -6i2) + 6x * (2i + 4x)) = 0
(-12ix + -6i2 + (2i * 6x + 4x * 6x)) = 0
(-12ix + -6i2 + (12ix + 24x2)) = 0
Reorder the terms:
(-12ix + 12ix + -6i2 + 24x2) = 0
Combine like terms: -12ix + 12ix = 0
(0 + -6i2 + 24x2) = 0
(-6i2 + 24x2) = 0
Solving
-6i2 + 24x2 = 0
Solving for variable 'i'.
Move all terms containing i to the left, all other terms to the right.
Add '-24x2' to each side of the equation.
-6i2 + 24x2 + -24x2 = 0 + -24x2
Combine like terms: 24x2 + -24x2 = 0
-6i2 + 0 = 0 + -24x2
-6i2 = 0 + -24x2
Remove the zero:
-6i2 = -24x2
Divide each side by '-6'.
i2 = 4x2
Simplifying
i2 = 4x2
Take the square root of each side:
i = {-2x, 2x}
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