(x-7)(8a-b)+(x+7)(8a-b)=0

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Solution for (x-7)(8a-b)+(x+7)(8a-b)=0 equation:


Simplifying
(x + -7)(8a + -1b) + (x + 7)(8a + -1b) = 0

Reorder the terms:
(-7 + x)(8a + -1b) + (x + 7)(8a + -1b) = 0

Multiply (-7 + x) * (8a + -1b)
(-7(8a + -1b) + x(8a + -1b)) + (x + 7)(8a + -1b) = 0
((8a * -7 + -1b * -7) + x(8a + -1b)) + (x + 7)(8a + -1b) = 0
((-56a + 7b) + x(8a + -1b)) + (x + 7)(8a + -1b) = 0
(-56a + 7b + (8a * x + -1b * x)) + (x + 7)(8a + -1b) = 0
(-56a + 7b + (8ax + -1bx)) + (x + 7)(8a + -1b) = 0

Reorder the terms:
(-56a + 8ax + 7b + -1bx) + (x + 7)(8a + -1b) = 0
(-56a + 8ax + 7b + -1bx) + (x + 7)(8a + -1b) = 0

Reorder the terms:
-56a + 8ax + 7b + -1bx + (7 + x)(8a + -1b) = 0

Multiply (7 + x) * (8a + -1b)
-56a + 8ax + 7b + -1bx + (7(8a + -1b) + x(8a + -1b)) = 0
-56a + 8ax + 7b + -1bx + ((8a * 7 + -1b * 7) + x(8a + -1b)) = 0
-56a + 8ax + 7b + -1bx + ((56a + -7b) + x(8a + -1b)) = 0
-56a + 8ax + 7b + -1bx + (56a + -7b + (8a * x + -1b * x)) = 0
-56a + 8ax + 7b + -1bx + (56a + -7b + (8ax + -1bx)) = 0

Reorder the terms:
-56a + 8ax + 7b + -1bx + (56a + 8ax + -7b + -1bx) = 0
-56a + 8ax + 7b + -1bx + (56a + 8ax + -7b + -1bx) = 0

Reorder the terms:
-56a + 56a + 8ax + 8ax + 7b + -7b + -1bx + -1bx = 0

Combine like terms: -56a + 56a = 0
0 + 8ax + 8ax + 7b + -7b + -1bx + -1bx = 0
8ax + 8ax + 7b + -7b + -1bx + -1bx = 0

Combine like terms: 8ax + 8ax = 16ax
16ax + 7b + -7b + -1bx + -1bx = 0

Combine like terms: 7b + -7b = 0
16ax + 0 + -1bx + -1bx = 0
16ax + -1bx + -1bx = 0

Combine like terms: -1bx + -1bx = -2bx
16ax + -2bx = 0

Solving
16ax + -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.
16ax + -2bx + 2bx = 0 + 2bx

Combine like terms: -2bx + 2bx = 0
16ax + 0 = 0 + 2bx
16ax = 0 + 2bx
Remove the zero:
16ax = 2bx

Divide each side by '16x'.
a = 0.125b

Simplifying
a = 0.125b

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