(18a^2-6a+16)by(3a-1)=

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Solution for (18a^2-6a+16)by(3a-1)= equation: 


Simplifying
(18a2 + -6a + 16) * by(3a + -1) = 0

Reorder the terms:
(16 + -6a + 18a2) * by(3a + -1) = 0

Reorder the terms:
(16 + -6a + 18a2) * by(-1 + 3a) = 0

Reorder the terms for easier multiplication:
by(16 + -6a + 18a2)(-1 + 3a) = 0

Multiply (16 + -6a + 18a2) * (-1 + 3a)
by(16(-1 + 3a) + -6a * (-1 + 3a) + 18a2 * (-1 + 3a)) = 0
by((-1 * 16 + 3a * 16) + -6a * (-1 + 3a) + 18a2 * (-1 + 3a)) = 0
by((-16 + 48a) + -6a * (-1 + 3a) + 18a2 * (-1 + 3a)) = 0
by(-16 + 48a + (-1 * -6a + 3a * -6a) + 18a2 * (-1 + 3a)) = 0
by(-16 + 48a + (6a + -18a2) + 18a2 * (-1 + 3a)) = 0
by(-16 + 48a + 6a + -18a2 + (-1 * 18a2 + 3a * 18a2)) = 0
by(-16 + 48a + 6a + -18a2 + (-18a2 + 54a3)) = 0

Combine like terms: 48a + 6a = 54a
by(-16 + 54a + -18a2 + -18a2 + 54a3) = 0

Combine like terms: -18a2 + -18a2 = -36a2
by(-16 + 54a + -36a2 + 54a3) = 0
(-16 * by + 54a * by + -36a2 * by + 54a3 * by) = 0

Reorder the terms:
(54aby + -36a2by + 54a3by + -16by) = 0
(54aby + -36a2by + 54a3by + -16by) = 0

Solving
54aby + -36a2by + 54a3by + -16by = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2by'.
2by(27a + -18a2 + 27a3 + -8) = 0

Ignore the factor 2.

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

Simplifying
by = 0

Solving
by = 0

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

Add '-1by' to each side of the equation.
by + -1by = 0 + -1by
Remove the zero:
0 = -1by

Simplifying
0 = -1by

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(27a + -18a2 + 27a3 + -8)' equal to zero and attempt to solve:

Simplifying
27a + -18a2 + 27a3 + -8 = 0

Reorder the terms:
-8 + 27a + -18a2 + 27a3 = 0

Solving
-8 + 27a + -18a2 + 27a3 = 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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