=(5x+9y+8z)(-12x+10y-15z)

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Solution for =(5x+9y+8z)(-12x+10y-15z) equation: 


Simplifying
0 = (5x + 9y + 8z)(-12x + 10y + -15z)

Multiply (5x + 9y + 8z) * (-12x + 10y + -15z)
0 = (5x * (-12x + 10y + -15z) + 9y * (-12x + 10y + -15z) + 8z * (-12x + 10y + -15z))
0 = ((-12x * 5x + 10y * 5x + -15z * 5x) + 9y * (-12x + 10y + -15z) + 8z * (-12x + 10y + -15z))

Reorder the terms:
0 = ((50xy + -75xz + -60x2) + 9y * (-12x + 10y + -15z) + 8z * (-12x + 10y + -15z))
0 = ((50xy + -75xz + -60x2) + 9y * (-12x + 10y + -15z) + 8z * (-12x + 10y + -15z))
0 = (50xy + -75xz + -60x2 + (-12x * 9y + 10y * 9y + -15z * 9y) + 8z * (-12x + 10y + -15z))

Reorder the terms:
0 = (50xy + -75xz + -60x2 + (-108xy + -135yz + 90y2) + 8z * (-12x + 10y + -15z))
0 = (50xy + -75xz + -60x2 + (-108xy + -135yz + 90y2) + 8z * (-12x + 10y + -15z))
0 = (50xy + -75xz + -60x2 + -108xy + -135yz + 90y2 + (-12x * 8z + 10y * 8z + -15z * 8z))
0 = (50xy + -75xz + -60x2 + -108xy + -135yz + 90y2 + (-96xz + 80yz + -120z2))

Reorder the terms:
0 = (50xy + -108xy + -75xz + -96xz + -60x2 + -135yz + 80yz + 90y2 + -120z2)

Combine like terms: 50xy + -108xy = -58xy
0 = (-58xy + -75xz + -96xz + -60x2 + -135yz + 80yz + 90y2 + -120z2)

Combine like terms: -75xz + -96xz = -171xz
0 = (-58xy + -171xz + -60x2 + -135yz + 80yz + 90y2 + -120z2)

Combine like terms: -135yz + 80yz = -55yz
0 = (-58xy + -171xz + -60x2 + -55yz + 90y2 + -120z2)

Solving
0 = -58xy + -171xz + -60x2 + -55yz + 90y2 + -120z2

Solving for variable 'x'.
Remove the zero:
58xy + 171xz + 60x2 + 55yz + -90y2 + 120z2 = -58xy + -171xz + -60x2 + -55yz + 90y2 + -120z2 + 58xy + 171xz + 60x2 + 55yz + -90y2 + 120z2

Reorder the terms:
58xy + 171xz + 60x2 + 55yz + -90y2 + 120z2 = -58xy + 58xy + -171xz + 171xz + -60x2 + 60x2 + -55yz + 55yz + 90y2 + -90y2 + -120z2 + 120z2

Combine like terms: -58xy + 58xy = 0
58xy + 171xz + 60x2 + 55yz + -90y2 + 120z2 = 0 + -171xz + 171xz + -60x2 + 60x2 + -55yz + 55yz + 90y2 + -90y2 + -120z2 + 120z2
58xy + 171xz + 60x2 + 55yz + -90y2 + 120z2 = -171xz + 171xz + -60x2 + 60x2 + -55yz + 55yz + 90y2 + -90y2 + -120z2 + 120z2

Combine like terms: -171xz + 171xz = 0
58xy + 171xz + 60x2 + 55yz + -90y2 + 120z2 = 0 + -60x2 + 60x2 + -55yz + 55yz + 90y2 + -90y2 + -120z2 + 120z2
58xy + 171xz + 60x2 + 55yz + -90y2 + 120z2 = -60x2 + 60x2 + -55yz + 55yz + 90y2 + -90y2 + -120z2 + 120z2

Combine like terms: -60x2 + 60x2 = 0
58xy + 171xz + 60x2 + 55yz + -90y2 + 120z2 = 0 + -55yz + 55yz + 90y2 + -90y2 + -120z2 + 120z2
58xy + 171xz + 60x2 + 55yz + -90y2 + 120z2 = -55yz + 55yz + 90y2 + -90y2 + -120z2 + 120z2

Combine like terms: -55yz + 55yz = 0
58xy + 171xz + 60x2 + 55yz + -90y2 + 120z2 = 0 + 90y2 + -90y2 + -120z2 + 120z2
58xy + 171xz + 60x2 + 55yz + -90y2 + 120z2 = 90y2 + -90y2 + -120z2 + 120z2

Combine like terms: 90y2 + -90y2 = 0
58xy + 171xz + 60x2 + 55yz + -90y2 + 120z2 = 0 + -120z2 + 120z2
58xy + 171xz + 60x2 + 55yz + -90y2 + 120z2 = -120z2 + 120z2

Combine like terms: -120z2 + 120z2 = 0
58xy + 171xz + 60x2 + 55yz + -90y2 + 120z2 = 0

The solution to this equation could not be determined.

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