(a+1)2+(a-1)2-2a^2=

Solution for (a+1)2+(a-1)2-2a^2= equation:

Simplifying
(a + 1) * 2 + (a + -1) * 2 + -2a2 = 0

Reorder the terms:
(1 + a) * 2 + (a + -1) * 2 + -2a2 = 0

Reorder the terms for easier multiplication:
2(1 + a) + (a + -1) * 2 + -2a2 = 0
(1 * 2 + a * 2) + (a + -1) * 2 + -2a2 = 0
(2 + 2a) + (a + -1) * 2 + -2a2 = 0

Reorder the terms:
2 + 2a + (-1 + a) * 2 + -2a2 = 0

Reorder the terms for easier multiplication:
2 + 2a + 2(-1 + a) + -2a2 = 0
2 + 2a + (-1 * 2 + a * 2) + -2a2 = 0
2 + 2a + (-2 + 2a) + -2a2 = 0

Reorder the terms:
2 + -2 + 2a + 2a + -2a2 = 0

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

Combine like terms: 2a + 2a = 4a
4a + -2a2 = 0

Solving
4a + -2a2 = 0

Solving for variable 'a'.

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

Ignore the factor 2.
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 '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

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

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

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

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

Simplifying
a = 2
Solution
a = {0, 2}