(x-8)(3a-b)+(x+8)(3a-b)=0

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Solution for (x-8)(3a-b)+(x+8)(3a-b)=0 equation: 


Simplifying
(x + -8)(3a + -1b) + (x + 8)(3a + -1b) = 0

Reorder the terms:
(-8 + x)(3a + -1b) + (x + 8)(3a + -1b) = 0

Multiply (-8 + x) * (3a + -1b)
(-8(3a + -1b) + x(3a + -1b)) + (x + 8)(3a + -1b) = 0
((3a * -8 + -1b * -8) + x(3a + -1b)) + (x + 8)(3a + -1b) = 0
((-24a + 8b) + x(3a + -1b)) + (x + 8)(3a + -1b) = 0
(-24a + 8b + (3a * x + -1b * x)) + (x + 8)(3a + -1b) = 0
(-24a + 8b + (3ax + -1bx)) + (x + 8)(3a + -1b) = 0

Reorder the terms:
(-24a + 3ax + 8b + -1bx) + (x + 8)(3a + -1b) = 0
(-24a + 3ax + 8b + -1bx) + (x + 8)(3a + -1b) = 0

Reorder the terms:
-24a + 3ax + 8b + -1bx + (8 + x)(3a + -1b) = 0

Multiply (8 + x) * (3a + -1b)
-24a + 3ax + 8b + -1bx + (8(3a + -1b) + x(3a + -1b)) = 0
-24a + 3ax + 8b + -1bx + ((3a * 8 + -1b * 8) + x(3a + -1b)) = 0
-24a + 3ax + 8b + -1bx + ((24a + -8b) + x(3a + -1b)) = 0
-24a + 3ax + 8b + -1bx + (24a + -8b + (3a * x + -1b * x)) = 0
-24a + 3ax + 8b + -1bx + (24a + -8b + (3ax + -1bx)) = 0

Reorder the terms:
-24a + 3ax + 8b + -1bx + (24a + 3ax + -8b + -1bx) = 0
-24a + 3ax + 8b + -1bx + (24a + 3ax + -8b + -1bx) = 0

Reorder the terms:
-24a + 24a + 3ax + 3ax + 8b + -8b + -1bx + -1bx = 0

Combine like terms: -24a + 24a = 0
0 + 3ax + 3ax + 8b + -8b + -1bx + -1bx = 0
3ax + 3ax + 8b + -8b + -1bx + -1bx = 0

Combine like terms: 3ax + 3ax = 6ax
6ax + 8b + -8b + -1bx + -1bx = 0

Combine like terms: 8b + -8b = 0
6ax + 0 + -1bx + -1bx = 0
6ax + -1bx + -1bx = 0

Combine like terms: -1bx + -1bx = -2bx
6ax + -2bx = 0

Solving
6ax + -2bx = 0

Solving for variable 'a'.

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

Add '2bx' to each side of the equation.
6ax + -2bx + 2bx = 0 + 2bx

Combine like terms: -2bx + 2bx = 0
6ax + 0 = 0 + 2bx
6ax = 0 + 2bx
Remove the zero:
6ax = 2bx

Divide each side by '6x'.
a = 0.3333333333b

Simplifying
a = 0.3333333333b

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