(3x+2y-4z)(6x-y+5z)=100

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Solution for (3x+2y-4z)(6x-y+5z)=100 equation: 


Simplifying
(3x + 2y + -4z)(6x + -1y + 5z) = 100

Multiply (3x + 2y + -4z) * (6x + -1y + 5z)
(3x * (6x + -1y + 5z) + 2y * (6x + -1y + 5z) + -4z * (6x + -1y + 5z)) = 100
((6x * 3x + -1y * 3x + 5z * 3x) + 2y * (6x + -1y + 5z) + -4z * (6x + -1y + 5z)) = 100

Reorder the terms:
((-3xy + 15xz + 18x2) + 2y * (6x + -1y + 5z) + -4z * (6x + -1y + 5z)) = 100
((-3xy + 15xz + 18x2) + 2y * (6x + -1y + 5z) + -4z * (6x + -1y + 5z)) = 100
(-3xy + 15xz + 18x2 + (6x * 2y + -1y * 2y + 5z * 2y) + -4z * (6x + -1y + 5z)) = 100

Reorder the terms:
(-3xy + 15xz + 18x2 + (12xy + 10yz + -2y2) + -4z * (6x + -1y + 5z)) = 100
(-3xy + 15xz + 18x2 + (12xy + 10yz + -2y2) + -4z * (6x + -1y + 5z)) = 100
(-3xy + 15xz + 18x2 + 12xy + 10yz + -2y2 + (6x * -4z + -1y * -4z + 5z * -4z)) = 100
(-3xy + 15xz + 18x2 + 12xy + 10yz + -2y2 + (-24xz + 4yz + -20z2)) = 100

Reorder the terms:
(-3xy + 12xy + 15xz + -24xz + 18x2 + 10yz + 4yz + -2y2 + -20z2) = 100

Combine like terms: -3xy + 12xy = 9xy
(9xy + 15xz + -24xz + 18x2 + 10yz + 4yz + -2y2 + -20z2) = 100

Combine like terms: 15xz + -24xz = -9xz
(9xy + -9xz + 18x2 + 10yz + 4yz + -2y2 + -20z2) = 100

Combine like terms: 10yz + 4yz = 14yz
(9xy + -9xz + 18x2 + 14yz + -2y2 + -20z2) = 100

Solving
9xy + -9xz + 18x2 + 14yz + -2y2 + -20z2 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + 9xy + -9xz + 18x2 + 14yz + -2y2 + -20z2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 9xy + -9xz + 18x2 + 14yz + -2y2 + -20z2 = 0

The solution to this equation could not be determined.

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