x^2-(a+2b)x+b^2+ab=0

Solution for x^2-(a+2b)x+b^2+ab=0 equation:

Simplifying
x2 + -1(a + 2b) * x + b2 + ab = 0

Reorder the terms for easier multiplication:
x2 + -1x(a + 2b) + b2 + ab = 0
x2 + (a * -1x + 2b * -1x) + b2 + ab = 0
x2 + (-1ax + -2bx) + b2 + ab = 0

Reorder the terms:
ab + -1ax + -2bx + b2 + x2 = 0

Solving
ab + -1ax + -2bx + b2 + x2 = 0

Solving for variable 'a'.

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

Add '2bx' to each side of the equation.
ab + -1ax + -2bx + b2 + 2bx + x2 = 0 + 2bx

Reorder the terms:
ab + -1ax + -2bx + 2bx + b2 + x2 = 0 + 2bx

Combine like terms: -2bx + 2bx = 0
ab + -1ax + 0 + b2 + x2 = 0 + 2bx
ab + -1ax + b2 + x2 = 0 + 2bx
Remove the zero:
ab + -1ax + b2 + x2 = 2bx

Add '-1b2' to each side of the equation.
ab + -1ax + b2 + -1b2 + x2 = 2bx + -1b2

Combine like terms: b2 + -1b2 = 0
ab + -1ax + 0 + x2 = 2bx + -1b2
ab + -1ax + x2 = 2bx + -1b2

Add '-1x2' to each side of the equation.
ab + -1ax + x2 + -1x2 = 2bx + -1b2 + -1x2

Combine like terms: x2 + -1x2 = 0
ab + -1ax + 0 = 2bx + -1b2 + -1x2
ab + -1ax = 2bx + -1b2 + -1x2

Reorder the terms:
ab + -1ax + -2bx + b2 + x2 = 2bx + -2bx + -1b2 + b2 + -1x2 + x2

Combine like terms: 2bx + -2bx = 0
ab + -1ax + -2bx + b2 + x2 = 0 + -1b2 + b2 + -1x2 + x2
ab + -1ax + -2bx + b2 + x2 = -1b2 + b2 + -1x2 + x2

Combine like terms: -1b2 + b2 = 0
ab + -1ax + -2bx + b2 + x2 = 0 + -1x2 + x2
ab + -1ax + -2bx + b2 + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
ab + -1ax + -2bx + b2 + x2 = 0

The solution to this equation could not be determined.