(8ax+3a)(4x^2-3ax-8a^2)=-(84a^3x^2)

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Solution for (8ax+3a)(4x^2-3ax-8a^2)=-(84a^3x^2) equation: 


Simplifying
(8ax + 3a)(4x2 + -3ax + -8a2) = -1(84a3x2)

Reorder the terms:
(3a + 8ax)(4x2 + -3ax + -8a2) = -1(84a3x2)

Reorder the terms:
(3a + 8ax)(-3ax + -8a2 + 4x2) = -1(84a3x2)

Multiply (3a + 8ax) * (-3ax + -8a2 + 4x2)
(3a * (-3ax + -8a2 + 4x2) + 8ax * (-3ax + -8a2 + 4x2)) = -1(84a3x2)
((-3ax * 3a + -8a2 * 3a + 4x2 * 3a) + 8ax * (-3ax + -8a2 + 4x2)) = -1(84a3x2)

Reorder the terms:
((12ax2 + -9a2x + -24a3) + 8ax * (-3ax + -8a2 + 4x2)) = -1(84a3x2)
((12ax2 + -9a2x + -24a3) + 8ax * (-3ax + -8a2 + 4x2)) = -1(84a3x2)
(12ax2 + -9a2x + -24a3 + (-3ax * 8ax + -8a2 * 8ax + 4x2 * 8ax)) = -1(84a3x2)

Reorder the terms:
(12ax2 + -9a2x + -24a3 + (32ax3 + -24a2x2 + -64a3x)) = -1(84a3x2)
(12ax2 + -9a2x + -24a3 + (32ax3 + -24a2x2 + -64a3x)) = -1(84a3x2)

Reorder the terms:
(12ax2 + 32ax3 + -9a2x + -24a2x2 + -24a3 + -64a3x) = -1(84a3x2)
(12ax2 + 32ax3 + -9a2x + -24a2x2 + -24a3 + -64a3x) = -1(84a3x2)

Remove parenthesis around (84a3x2)
12ax2 + 32ax3 + -9a2x + -24a2x2 + -24a3 + -64a3x = -1 * 84a3x2

Multiply -1 * 84
12ax2 + 32ax3 + -9a2x + -24a2x2 + -24a3 + -64a3x = -84a3x2

Solving
12ax2 + 32ax3 + -9a2x + -24a2x2 + -24a3 + -64a3x = -84a3x2

Solving for variable 'a'.

Combine like terms: -84a3x2 + 84a3x2 = 0
12ax2 + 32ax3 + -9a2x + -24a2x2 + -24a3 + -64a3x + 84a3x2 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(12x2 + 32x3 + -9ax + -24ax2 + -24a2 + -64a2x + 84a2x2) = 0


Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0

Subproblem 2
Set the factor '(12x2 + 32x3 + -9ax + -24ax2 + -24a2 + -64a2x + 84a2x2)' equal to zero and attempt to solve:

Simplifying
12x2 + 32x3 + -9ax + -24ax2 + -24a2 + -64a2x + 84a2x2 = 0

Reorder the terms:
-9ax + -24ax2 + -24a2 + -64a2x + 84a2x2 + 12x2 + 32x3 = 0

Solving
-9ax + -24ax2 + -24a2 + -64a2x + 84a2x2 + 12x2 + 32x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}

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