15ax-10bx+5cx+12ay-8by+4cy+15az-10bz+5cz=0

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Solution for 15ax-10bx+5cx+12ay-8by+4cy+15az-10bz+5cz=0 equation:


Simplifying
15ax + -10bx + 5cx + 12ay + -8by + 4cy + 15az + -10bz + 5cz = 0

Reorder the terms:
15ax + 12ay + 15az + -10bx + -8by + -10bz + 5cx + 4cy + 5cz = 0

Solving
15ax + 12ay + 15az + -10bx + -8by + -10bz + 5cx + 4cy + 5cz = 0

Solving for variable 'a'.

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

Add '10bx' to each side of the equation.
15ax + 12ay + 15az + -10bx + -8by + -10bz + 5cx + 4cy + 10bx + 5cz = 0 + 10bx

Reorder the terms:
15ax + 12ay + 15az + -10bx + 10bx + -8by + -10bz + 5cx + 4cy + 5cz = 0 + 10bx

Combine like terms: -10bx + 10bx = 0
15ax + 12ay + 15az + 0 + -8by + -10bz + 5cx + 4cy + 5cz = 0 + 10bx
15ax + 12ay + 15az + -8by + -10bz + 5cx + 4cy + 5cz = 0 + 10bx
Remove the zero:
15ax + 12ay + 15az + -8by + -10bz + 5cx + 4cy + 5cz = 10bx

Add '8by' to each side of the equation.
15ax + 12ay + 15az + -8by + -10bz + 5cx + 4cy + 8by + 5cz = 10bx + 8by

Reorder the terms:
15ax + 12ay + 15az + -8by + 8by + -10bz + 5cx + 4cy + 5cz = 10bx + 8by

Combine like terms: -8by + 8by = 0
15ax + 12ay + 15az + 0 + -10bz + 5cx + 4cy + 5cz = 10bx + 8by
15ax + 12ay + 15az + -10bz + 5cx + 4cy + 5cz = 10bx + 8by

Add '10bz' to each side of the equation.
15ax + 12ay + 15az + -10bz + 5cx + 4cy + 10bz + 5cz = 10bx + 8by + 10bz

Reorder the terms:
15ax + 12ay + 15az + -10bz + 10bz + 5cx + 4cy + 5cz = 10bx + 8by + 10bz

Combine like terms: -10bz + 10bz = 0
15ax + 12ay + 15az + 0 + 5cx + 4cy + 5cz = 10bx + 8by + 10bz
15ax + 12ay + 15az + 5cx + 4cy + 5cz = 10bx + 8by + 10bz

Add '-5cx' to each side of the equation.
15ax + 12ay + 15az + 5cx + 4cy + -5cx + 5cz = 10bx + 8by + 10bz + -5cx

Reorder the terms:
15ax + 12ay + 15az + 5cx + -5cx + 4cy + 5cz = 10bx + 8by + 10bz + -5cx

Combine like terms: 5cx + -5cx = 0
15ax + 12ay + 15az + 0 + 4cy + 5cz = 10bx + 8by + 10bz + -5cx
15ax + 12ay + 15az + 4cy + 5cz = 10bx + 8by + 10bz + -5cx

Add '-4cy' to each side of the equation.
15ax + 12ay + 15az + 4cy + -4cy + 5cz = 10bx + 8by + 10bz + -5cx + -4cy

Combine like terms: 4cy + -4cy = 0
15ax + 12ay + 15az + 0 + 5cz = 10bx + 8by + 10bz + -5cx + -4cy
15ax + 12ay + 15az + 5cz = 10bx + 8by + 10bz + -5cx + -4cy

Add '-5cz' to each side of the equation.
15ax + 12ay + 15az + 5cz + -5cz = 10bx + 8by + 10bz + -5cx + -4cy + -5cz

Combine like terms: 5cz + -5cz = 0
15ax + 12ay + 15az + 0 = 10bx + 8by + 10bz + -5cx + -4cy + -5cz
15ax + 12ay + 15az = 10bx + 8by + 10bz + -5cx + -4cy + -5cz

Reorder the terms:
15ax + 12ay + 15az + -10bx + -8by + -10bz + 5cx + 4cy + 5cz = 10bx + -10bx + 8by + -8by + 10bz + -10bz + -5cx + 5cx + -4cy + 4cy + -5cz + 5cz

Combine like terms: 10bx + -10bx = 0
15ax + 12ay + 15az + -10bx + -8by + -10bz + 5cx + 4cy + 5cz = 0 + 8by + -8by + 10bz + -10bz + -5cx + 5cx + -4cy + 4cy + -5cz + 5cz
15ax + 12ay + 15az + -10bx + -8by + -10bz + 5cx + 4cy + 5cz = 8by + -8by + 10bz + -10bz + -5cx + 5cx + -4cy + 4cy + -5cz + 5cz

Combine like terms: 8by + -8by = 0
15ax + 12ay + 15az + -10bx + -8by + -10bz + 5cx + 4cy + 5cz = 0 + 10bz + -10bz + -5cx + 5cx + -4cy + 4cy + -5cz + 5cz
15ax + 12ay + 15az + -10bx + -8by + -10bz + 5cx + 4cy + 5cz = 10bz + -10bz + -5cx + 5cx + -4cy + 4cy + -5cz + 5cz

Combine like terms: 10bz + -10bz = 0
15ax + 12ay + 15az + -10bx + -8by + -10bz + 5cx + 4cy + 5cz = 0 + -5cx + 5cx + -4cy + 4cy + -5cz + 5cz
15ax + 12ay + 15az + -10bx + -8by + -10bz + 5cx + 4cy + 5cz = -5cx + 5cx + -4cy + 4cy + -5cz + 5cz

Combine like terms: -5cx + 5cx = 0
15ax + 12ay + 15az + -10bx + -8by + -10bz + 5cx + 4cy + 5cz = 0 + -4cy + 4cy + -5cz + 5cz
15ax + 12ay + 15az + -10bx + -8by + -10bz + 5cx + 4cy + 5cz = -4cy + 4cy + -5cz + 5cz

Combine like terms: -4cy + 4cy = 0
15ax + 12ay + 15az + -10bx + -8by + -10bz + 5cx + 4cy + 5cz = 0 + -5cz + 5cz
15ax + 12ay + 15az + -10bx + -8by + -10bz + 5cx + 4cy + 5cz = -5cz + 5cz

Combine like terms: -5cz + 5cz = 0
15ax + 12ay + 15az + -10bx + -8by + -10bz + 5cx + 4cy + 5cz = 0

The solution to this equation could not be determined.

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