6(8a-b)8(7b-8a)=

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Solution for 6(8a-b)8(7b-8a)= equation: 


Simplifying
6(8a + -1b) * 8(7b + -8a) = 0

Reorder the terms:
6(8a + -1b) * 8(-8a + 7b) = 0

Reorder the terms for easier multiplication:
6 * 8(8a + -1b)(-8a + 7b) = 0

Multiply 6 * 8
48(8a + -1b)(-8a + 7b) = 0

Multiply (8a + -1b) * (-8a + 7b)
48(8a * (-8a + 7b) + -1b * (-8a + 7b)) = 0
48((-8a * 8a + 7b * 8a) + -1b * (-8a + 7b)) = 0

Reorder the terms:
48((56ab + -64a2) + -1b * (-8a + 7b)) = 0
48((56ab + -64a2) + -1b * (-8a + 7b)) = 0
48(56ab + -64a2 + (-8a * -1b + 7b * -1b)) = 0
48(56ab + -64a2 + (8ab + -7b2)) = 0

Reorder the terms:
48(56ab + 8ab + -64a2 + -7b2) = 0

Combine like terms: 56ab + 8ab = 64ab
48(64ab + -64a2 + -7b2) = 0
(64ab * 48 + -64a2 * 48 + -7b2 * 48) = 0
(3072ab + -3072a2 + -336b2) = 0

Solving
3072ab + -3072a2 + -336b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '48'.
48(64ab + -64a2 + -7b2) = 0

Factor a trinomial.
48((-8a + b)(8a + -7b)) = 0

Ignore the factor 48.

Subproblem 1
Set the factor '(-8a + b)' equal to zero and attempt to solve:

Simplifying
-8a + b = 0

Solving
-8a + b = 0

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

Add '-1b' to each side of the equation.
-8a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
-8a + 0 = 0 + -1b
-8a = 0 + -1b
Remove the zero:
-8a = -1b

Divide each side by '-8'.
a = 0.125b

Simplifying
a = 0.125b

Subproblem 2
Set the factor '(8a + -7b)' equal to zero and attempt to solve:

Simplifying
8a + -7b = 0

Solving
8a + -7b = 0

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

Add '7b' to each side of the equation.
8a + -7b + 7b = 0 + 7b

Combine like terms: -7b + 7b = 0
8a + 0 = 0 + 7b
8a = 0 + 7b
Remove the zero:
8a = 7b

Divide each side by '8'.
a = 0.875b

Simplifying
a = 0.875b
Solution
a = {0.125b, 0.875b}

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