2a(x^2-y)-5b(x^2-y)+c(x^2+y)=0

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Solution for 2a(x^2-y)-5b(x^2-y)+c(x^2+y)=0 equation: 


Simplifying
2a(x2 + -1y) + -5b(x2 + -1y) + c(x2 + y) = 0
(x2 * 2a + -1y * 2a) + -5b(x2 + -1y) + c(x2 + y) = 0
(2ax2 + -2ay) + -5b(x2 + -1y) + c(x2 + y) = 0
2ax2 + -2ay + (x2 * -5b + -1y * -5b) + c(x2 + y) = 0
2ax2 + -2ay + (-5bx2 + 5by) + c(x2 + y) = 0
2ax2 + -2ay + -5bx2 + 5by + (x2 * c + y * c) = 0
2ax2 + -2ay + -5bx2 + 5by + (cx2 + cy) = 0

Solving
2ax2 + -2ay + -5bx2 + 5by + cx2 + cy = 0

Solving for variable 'a'.

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

Add '5bx2' to each side of the equation.
2ax2 + -2ay + -5bx2 + 5by + cx2 + 5bx2 + cy = 0 + 5bx2

Reorder the terms:
2ax2 + -2ay + -5bx2 + 5bx2 + 5by + cx2 + cy = 0 + 5bx2

Combine like terms: -5bx2 + 5bx2 = 0
2ax2 + -2ay + 0 + 5by + cx2 + cy = 0 + 5bx2
2ax2 + -2ay + 5by + cx2 + cy = 0 + 5bx2
Remove the zero:
2ax2 + -2ay + 5by + cx2 + cy = 5bx2

Add '-5by' to each side of the equation.
2ax2 + -2ay + 5by + cx2 + -5by + cy = 5bx2 + -5by

Reorder the terms:
2ax2 + -2ay + 5by + -5by + cx2 + cy = 5bx2 + -5by

Combine like terms: 5by + -5by = 0
2ax2 + -2ay + 0 + cx2 + cy = 5bx2 + -5by
2ax2 + -2ay + cx2 + cy = 5bx2 + -5by

Add '-1cx2' to each side of the equation.
2ax2 + -2ay + cx2 + -1cx2 + cy = 5bx2 + -5by + -1cx2

Combine like terms: cx2 + -1cx2 = 0
2ax2 + -2ay + 0 + cy = 5bx2 + -5by + -1cx2
2ax2 + -2ay + cy = 5bx2 + -5by + -1cx2

Add '-1cy' to each side of the equation.
2ax2 + -2ay + cy + -1cy = 5bx2 + -5by + -1cx2 + -1cy

Combine like terms: cy + -1cy = 0
2ax2 + -2ay + 0 = 5bx2 + -5by + -1cx2 + -1cy
2ax2 + -2ay = 5bx2 + -5by + -1cx2 + -1cy

Reorder the terms:
2ax2 + -2ay + -5bx2 + 5by + cx2 + cy = 5bx2 + -5bx2 + -5by + 5by + -1cx2 + cx2 + -1cy + cy

Combine like terms: 5bx2 + -5bx2 = 0
2ax2 + -2ay + -5bx2 + 5by + cx2 + cy = 0 + -5by + 5by + -1cx2 + cx2 + -1cy + cy
2ax2 + -2ay + -5bx2 + 5by + cx2 + cy = -5by + 5by + -1cx2 + cx2 + -1cy + cy

Combine like terms: -5by + 5by = 0
2ax2 + -2ay + -5bx2 + 5by + cx2 + cy = 0 + -1cx2 + cx2 + -1cy + cy
2ax2 + -2ay + -5bx2 + 5by + cx2 + cy = -1cx2 + cx2 + -1cy + cy

Combine like terms: -1cx2 + cx2 = 0
2ax2 + -2ay + -5bx2 + 5by + cx2 + cy = 0 + -1cy + cy
2ax2 + -2ay + -5bx2 + 5by + cx2 + cy = -1cy + cy

Combine like terms: -1cy + cy = 0
2ax2 + -2ay + -5bx2 + 5by + cx2 + cy = 0

The solution to this equation could not be determined.

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