(6a+1)x(2a+3)=xa^2+ya+z

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Solution for (6a+1)x(2a+3)=xa^2+ya+z equation: 


Simplifying
(6a + 1) * x(2a + 3) = xa2 + ya + z

Reorder the terms:
(1 + 6a) * x(2a + 3) = xa2 + ya + z

Reorder the terms:
(1 + 6a) * x(3 + 2a) = xa2 + ya + z

Reorder the terms for easier multiplication:
x(1 + 6a)(3 + 2a) = xa2 + ya + z

Multiply (1 + 6a) * (3 + 2a)
x(1(3 + 2a) + 6a * (3 + 2a)) = xa2 + ya + z
x((3 * 1 + 2a * 1) + 6a * (3 + 2a)) = xa2 + ya + z
x((3 + 2a) + 6a * (3 + 2a)) = xa2 + ya + z
x(3 + 2a + (3 * 6a + 2a * 6a)) = xa2 + ya + z
x(3 + 2a + (18a + 12a2)) = xa2 + ya + z

Combine like terms: 2a + 18a = 20a
x(3 + 20a + 12a2) = xa2 + ya + z
(3 * x + 20a * x + 12a2 * x) = xa2 + ya + z

Reorder the terms:
(20ax + 12a2x + 3x) = xa2 + ya + z
(20ax + 12a2x + 3x) = xa2 + ya + z

Reorder the terms:
20ax + 12a2x + 3x = ay + a2x + z

Solving
20ax + 12a2x + 3x = ay + a2x + z

Solving for variable 'a'.

Reorder the terms:
20ax + -1ay + 12a2x + -1a2x + 3x + -1z = ay + a2x + z + -1ay + -1a2x + -1z

Combine like terms: 12a2x + -1a2x = 11a2x
20ax + -1ay + 11a2x + 3x + -1z = ay + a2x + z + -1ay + -1a2x + -1z

Reorder the terms:
20ax + -1ay + 11a2x + 3x + -1z = ay + -1ay + a2x + -1a2x + z + -1z

Combine like terms: ay + -1ay = 0
20ax + -1ay + 11a2x + 3x + -1z = 0 + a2x + -1a2x + z + -1z
20ax + -1ay + 11a2x + 3x + -1z = a2x + -1a2x + z + -1z

Combine like terms: a2x + -1a2x = 0
20ax + -1ay + 11a2x + 3x + -1z = 0 + z + -1z
20ax + -1ay + 11a2x + 3x + -1z = z + -1z

Combine like terms: z + -1z = 0
20ax + -1ay + 11a2x + 3x + -1z = 0

The solution to this equation could not be determined.

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