(8yi-2)(3-i)=-(8yi+2)(3-i)

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Solution for (8yi-2)(3-i)=-(8yi+2)(3-i) equation:


Simplifying
(8yi + -2)(3 + -1i) = -1(8yi + 2)(3 + -1i)

Reorder the terms:
(-2 + 8iy)(3 + -1i) = -1(8yi + 2)(3 + -1i)

Multiply (-2 + 8iy) * (3 + -1i)
(-2(3 + -1i) + 8iy * (3 + -1i)) = -1(8yi + 2)(3 + -1i)
((3 * -2 + -1i * -2) + 8iy * (3 + -1i)) = -1(8yi + 2)(3 + -1i)
((-6 + 2i) + 8iy * (3 + -1i)) = -1(8yi + 2)(3 + -1i)
(-6 + 2i + (3 * 8iy + -1i * 8iy)) = -1(8yi + 2)(3 + -1i)
(-6 + 2i + (24iy + -8i2y)) = -1(8yi + 2)(3 + -1i)
(-6 + 2i + 24iy + -8i2y) = -1(8yi + 2)(3 + -1i)

Reorder the terms:
-6 + 2i + 24iy + -8i2y = -1(2 + 8iy)(3 + -1i)

Multiply (2 + 8iy) * (3 + -1i)
-6 + 2i + 24iy + -8i2y = -1(2(3 + -1i) + 8iy * (3 + -1i))
-6 + 2i + 24iy + -8i2y = -1((3 * 2 + -1i * 2) + 8iy * (3 + -1i))
-6 + 2i + 24iy + -8i2y = -1((6 + -2i) + 8iy * (3 + -1i))
-6 + 2i + 24iy + -8i2y = -1(6 + -2i + (3 * 8iy + -1i * 8iy))
-6 + 2i + 24iy + -8i2y = -1(6 + -2i + (24iy + -8i2y))
-6 + 2i + 24iy + -8i2y = -1(6 + -2i + 24iy + -8i2y)
-6 + 2i + 24iy + -8i2y = (6 * -1 + -2i * -1 + 24iy * -1 + -8i2y * -1)
-6 + 2i + 24iy + -8i2y = (-6 + 2i + -24iy + 8i2y)

Add '6' to each side of the equation.
-6 + 2i + 24iy + 6 + -8i2y = -6 + 2i + -24iy + 6 + 8i2y

Reorder the terms:
-6 + 6 + 2i + 24iy + -8i2y = -6 + 2i + -24iy + 6 + 8i2y

Combine like terms: -6 + 6 = 0
0 + 2i + 24iy + -8i2y = -6 + 2i + -24iy + 6 + 8i2y
2i + 24iy + -8i2y = -6 + 2i + -24iy + 6 + 8i2y

Reorder the terms:
2i + 24iy + -8i2y = -6 + 6 + 2i + -24iy + 8i2y

Combine like terms: -6 + 6 = 0
2i + 24iy + -8i2y = 0 + 2i + -24iy + 8i2y
2i + 24iy + -8i2y = 2i + -24iy + 8i2y

Add '-2i' to each side of the equation.
2i + 24iy + -2i + -8i2y = 2i + -24iy + -2i + 8i2y

Reorder the terms:
2i + -2i + 24iy + -8i2y = 2i + -24iy + -2i + 8i2y

Combine like terms: 2i + -2i = 0
0 + 24iy + -8i2y = 2i + -24iy + -2i + 8i2y
24iy + -8i2y = 2i + -24iy + -2i + 8i2y

Reorder the terms:
24iy + -8i2y = 2i + -2i + -24iy + 8i2y

Combine like terms: 2i + -2i = 0
24iy + -8i2y = 0 + -24iy + 8i2y
24iy + -8i2y = -24iy + 8i2y

Solving
24iy + -8i2y = -24iy + 8i2y

Solving for variable 'i'.

Reorder the terms:
24iy + 24iy + -8i2y + -8i2y = -24iy + 8i2y + 24iy + -8i2y

Combine like terms: 24iy + 24iy = 48iy
48iy + -8i2y + -8i2y = -24iy + 8i2y + 24iy + -8i2y

Combine like terms: -8i2y + -8i2y = -16i2y
48iy + -16i2y = -24iy + 8i2y + 24iy + -8i2y

Reorder the terms:
48iy + -16i2y = -24iy + 24iy + 8i2y + -8i2y

Combine like terms: -24iy + 24iy = 0
48iy + -16i2y = 0 + 8i2y + -8i2y
48iy + -16i2y = 8i2y + -8i2y

Combine like terms: 8i2y + -8i2y = 0
48iy + -16i2y = 0

Factor out the Greatest Common Factor (GCF), '16iy'.
16iy(3 + -1i) = 0

Ignore the factor 16.

Subproblem 1

Set the factor 'iy' equal to zero and attempt to solve: Simplifying iy = 0 Solving iy = 0 Move all terms containing i to the left, all other terms to the right. Simplifying iy = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(3 + -1i)' equal to zero and attempt to solve: Simplifying 3 + -1i = 0 Solving 3 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1i = 0 + -3 -1i = 0 + -3 Combine like terms: 0 + -3 = -3 -1i = -3 Divide each side by '-1'. i = 3 Simplifying i = 3

Solution

i = {3}

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