(10ac-5b+7)(4ac-2b-8)=0

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Solution for (10ac-5b+7)(4ac-2b-8)=0 equation: 


Simplifying
(10ac + -5b + 7)(4ac + -2b + -8) = 0

Reorder the terms:
(7 + 10ac + -5b)(4ac + -2b + -8) = 0

Reorder the terms:
(7 + 10ac + -5b)(-8 + 4ac + -2b) = 0

Multiply (7 + 10ac + -5b) * (-8 + 4ac + -2b)
(7(-8 + 4ac + -2b) + 10ac * (-8 + 4ac + -2b) + -5b * (-8 + 4ac + -2b)) = 0
((-8 * 7 + 4ac * 7 + -2b * 7) + 10ac * (-8 + 4ac + -2b) + -5b * (-8 + 4ac + -2b)) = 0
((-56 + 28ac + -14b) + 10ac * (-8 + 4ac + -2b) + -5b * (-8 + 4ac + -2b)) = 0
(-56 + 28ac + -14b + (-8 * 10ac + 4ac * 10ac + -2b * 10ac) + -5b * (-8 + 4ac + -2b)) = 0

Reorder the terms:
(-56 + 28ac + -14b + (-20abc + -80ac + 40a2c2) + -5b * (-8 + 4ac + -2b)) = 0
(-56 + 28ac + -14b + (-20abc + -80ac + 40a2c2) + -5b * (-8 + 4ac + -2b)) = 0
(-56 + 28ac + -14b + -20abc + -80ac + 40a2c2 + (-8 * -5b + 4ac * -5b + -2b * -5b)) = 0

Reorder the terms:
(-56 + 28ac + -14b + -20abc + -80ac + 40a2c2 + (-20abc + 40b + 10b2)) = 0
(-56 + 28ac + -14b + -20abc + -80ac + 40a2c2 + (-20abc + 40b + 10b2)) = 0

Reorder the terms:
(-56 + -20abc + -20abc + 28ac + -80ac + 40a2c2 + -14b + 40b + 10b2) = 0

Combine like terms: -20abc + -20abc = -40abc
(-56 + -40abc + 28ac + -80ac + 40a2c2 + -14b + 40b + 10b2) = 0

Combine like terms: 28ac + -80ac = -52ac
(-56 + -40abc + -52ac + 40a2c2 + -14b + 40b + 10b2) = 0

Combine like terms: -14b + 40b = 26b
(-56 + -40abc + -52ac + 40a2c2 + 26b + 10b2) = 0

Solving
-56 + -40abc + -52ac + 40a2c2 + 26b + 10b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-28 + -20abc + -26ac + 20a2c2 + 13b + 5b2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-28 + -20abc + -26ac + 20a2c2 + 13b + 5b2)' equal to zero and attempt to solve:

Simplifying
-28 + -20abc + -26ac + 20a2c2 + 13b + 5b2 = 0

Solving
-28 + -20abc + -26ac + 20a2c2 + 13b + 5b2 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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