(x^2+4a)=x^2+2ax+2a(x+2a)

Solution for (x^2+4a)=x^2+2ax+2a(x+2a) equation:

Simplifying
(x2 + 4a) = x2 + 2ax + 2a(x + 2a)

Reorder the terms:
(4a + x2) = x2 + 2ax + 2a(x + 2a)

Remove parenthesis around (4a + x2)
4a + x2 = x2 + 2ax + 2a(x + 2a)

Reorder the terms:
4a + x2 = x2 + 2ax + 2a(2a + x)
4a + x2 = x2 + 2ax + (2a * 2a + x * 2a)

Reorder the terms:
4a + x2 = x2 + 2ax + (2ax + 4a2)
4a + x2 = x2 + 2ax + (2ax + 4a2)

Reorder the terms:
4a + x2 = 2ax + 2ax + 4a2 + x2

Combine like terms: 2ax + 2ax = 4ax
4a + x2 = 4ax + 4a2 + x2

Add '-1x2' to each side of the equation.
4a + x2 + -1x2 = 4ax + 4a2 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4a + 0 = 4ax + 4a2 + x2 + -1x2
4a = 4ax + 4a2 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4a = 4ax + 4a2 + 0
4a = 4ax + 4a2

Solving
4a = 4ax + 4a2

Solving for variable 'a'.

Reorder the terms:
4a + -4ax + -4a2 = 4ax + -4ax + 4a2 + -4a2

Combine like terms: 4ax + -4ax = 0
4a + -4ax + -4a2 = 0 + 4a2 + -4a2
4a + -4ax + -4a2 = 4a2 + -4a2

Combine like terms: 4a2 + -4a2 = 0
4a + -4ax + -4a2 = 0

Factor out the Greatest Common Factor (GCF), '4a'.
4a(1 + -1x + -1a) = 0

Ignore the factor 4.
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 + -1x + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1x + -1a = 0

Reorder the terms:
1 + -1a + -1x = 0

Solving
1 + -1a + -1x = 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 + -1x = 0 + -1

Reorder the terms:
1 + -1 + -1a + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1a + -1x = 0 + -1
-1a + -1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1a + -1x = -1

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

Combine like terms: -1x + x = 0
-1a + 0 = -1 + x
-1a = -1 + x

Divide each side by '-1'.
a = 1 + -1x

Simplifying
a = 1 + -1x
Solution
a = {0, 1 + -1x}