A^2+n+8b^2=(a+b)(a+8b)

Solution for A^2+n+8b^2=(a+b)(a+8b) equation:

Simplifying
A2 + n + 8b2 = (a + b)(a + 8b)

Reorder the terms:
A2 + 8b2 + n = (a + b)(a + 8b)

Multiply (a + b) * (a + 8b)
A2 + 8b2 + n = (a(a + 8b) + b(a + 8b))
A2 + 8b2 + n = ((a * a + 8b * a) + b(a + 8b))

Reorder the terms:
A2 + 8b2 + n = ((8ab + a2) + b(a + 8b))
A2 + 8b2 + n = ((8ab + a2) + b(a + 8b))
A2 + 8b2 + n = (8ab + a2 + (a * b + 8b * b))
A2 + 8b2 + n = (8ab + a2 + (ab + 8b2))

Reorder the terms:
A2 + 8b2 + n = (8ab + ab + a2 + 8b2)

Combine like terms: 8ab + ab = 9ab
A2 + 8b2 + n = (9ab + a2 + 8b2)

Add '-8b2' to each side of the equation.
A2 + 8b2 + -8b2 + n = 9ab + a2 + 8b2 + -8b2

Combine like terms: 8b2 + -8b2 = 0
A2 + 0 + n = 9ab + a2 + 8b2 + -8b2
A2 + n = 9ab + a2 + 8b2 + -8b2

Combine like terms: 8b2 + -8b2 = 0
A2 + n = 9ab + a2 + 0
A2 + n = 9ab + a2

Solving
A2 + n = 9ab + a2

Solving for variable 'A'.

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

Add '-1n' to each side of the equation.
A2 + n + -1n = 9ab + a2 + -1n

Combine like terms: n + -1n = 0
A2 + 0 = 9ab + a2 + -1n
A2 = 9ab + a2 + -1n

Simplifying
A2 = 9ab + a2 + -1n

Reorder the terms:
A2 + -9ab + -1a2 + n = 9ab + -9ab + a2 + -1a2 + -1n + n

Combine like terms: 9ab + -9ab = 0
A2 + -9ab + -1a2 + n = 0 + a2 + -1a2 + -1n + n
A2 + -9ab + -1a2 + n = a2 + -1a2 + -1n + n

Combine like terms: a2 + -1a2 = 0
A2 + -9ab + -1a2 + n = 0 + -1n + n
A2 + -9ab + -1a2 + n = -1n + n

Combine like terms: -1n + n = 0
A2 + -9ab + -1a2 + n = 0

The solution to this equation could not be determined.