a(a+b)-2a(a-b)=

Solution for a(a+b)-2a(a-b)= equation:

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

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

Reorder the terms:
ab + a2 + (2ab + -2a2) = 0
ab + a2 + (2ab + -2a2) = 0

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

Combine like terms: ab + 2ab = 3ab
3ab + a2 + -2a2 = 0

Combine like terms: a2 + -2a2 = -1a2
3ab + -1a2 = 0

Solving
3ab + -1a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(3b + -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 '(3b + -1a)' equal to zero and attempt to solve:

Simplifying
3b + -1a = 0

Reorder the terms:
-1a + 3b = 0

Solving
-1a + 3b = 0

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

Add '-3b' to each side of the equation.
-1a + 3b + -3b = 0 + -3b

Combine like terms: 3b + -3b = 0
-1a + 0 = 0 + -3b
-1a = 0 + -3b
Remove the zero:
-1a = -3b

Divide each side by '-1'.
a = 3b

Simplifying
a = 3b
Solution
a = {0, 3b}