(a+b^2)=a^2+2ab+b^2

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

Simplifying
(a + b2) = a2 + 2ab + b2

Remove parenthesis around (a + b2)
a + b2 = a2 + 2ab + b2

Reorder the terms:
a + b2 = 2ab + a2 + b2

Add '-1b2' to each side of the equation.
a + b2 + -1b2 = 2ab + a2 + b2 + -1b2

Combine like terms: b2 + -1b2 = 0
a + 0 = 2ab + a2 + b2 + -1b2
a = 2ab + a2 + b2 + -1b2

Combine like terms: b2 + -1b2 = 0
a = 2ab + a2 + 0
a = 2ab + a2

Solving
a = 2ab + a2

Solving for variable 'a'.

Reorder the terms:
a + -2ab + -1a2 = 2ab + -2ab + a2 + -1a2

Combine like terms: 2ab + -2ab = 0
a + -2ab + -1a2 = 0 + a2 + -1a2
a + -2ab + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
a + -2ab + -1a2 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(1 + -2b + -1a) = 0

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(1 + -2b + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -2b + -1a = 0

Reorder the terms:
1 + -1a + -2b = 0

Solving
1 + -1a + -2b = 0

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

Add '-1' to each side of the equation.
1 + -1a + -1 + -2b = 0 + -1

Reorder the terms:
1 + -1 + -1a + -2b = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1a + -2b = 0 + -1
-1a + -2b = 0 + -1

Combine like terms: 0 + -1 = -1
-1a + -2b = -1

Add '2b' to each side of the equation.
-1a + -2b + 2b = -1 + 2b

Combine like terms: -2b + 2b = 0
-1a + 0 = -1 + 2b
-1a = -1 + 2b

Divide each side by '-1'.
a = 1 + -2b

Simplifying
a = 1 + -2b
Solution
a = {0, 1 + -2b}