ax^2+by^2=(a+b)z^2

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Solution for ax^2+by^2=(a+b)z^2 equation: 


Simplifying
ax2 + by2 = (a + b) * z2

Reorder the terms for easier multiplication:
ax2 + by2 = z2(a + b)
ax2 + by2 = (a * z2 + b * z2)
ax2 + by2 = (az2 + bz2)

Solving
ax2 + by2 = az2 + bz2

Solving for variable 'a'.

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

Add '-1az2' to each side of the equation.
ax2 + -1az2 + by2 = az2 + -1az2 + bz2

Combine like terms: az2 + -1az2 = 0
ax2 + -1az2 + by2 = 0 + bz2
ax2 + -1az2 + by2 = bz2

Add '-1by2' to each side of the equation.
ax2 + -1az2 + by2 + -1by2 = -1by2 + bz2

Combine like terms: by2 + -1by2 = 0
ax2 + -1az2 + 0 = -1by2 + bz2
ax2 + -1az2 = -1by2 + bz2

Reorder the terms:
ax2 + -1az2 + by2 + -1bz2 = -1by2 + by2 + bz2 + -1bz2

Combine like terms: -1by2 + by2 = 0
ax2 + -1az2 + by2 + -1bz2 = 0 + bz2 + -1bz2
ax2 + -1az2 + by2 + -1bz2 = bz2 + -1bz2

Combine like terms: bz2 + -1bz2 = 0
ax2 + -1az2 + by2 + -1bz2 = 0

The solution to this equation could not be determined.

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