2a*(a-b)=a^2-3ab

Solution for 2a*(a-b)=a^2-3ab equation:

Simplifying
2a(a + -1b) = a2 + -3ab
(a * 2a + -1b * 2a) = a2 + -3ab

Reorder the terms:
(-2ab + 2a2) = a2 + -3ab
(-2ab + 2a2) = a2 + -3ab

Reorder the terms:
-2ab + 2a2 = -3ab + a2

Solving
-2ab + 2a2 = -3ab + a2

Solving for variable 'a'.

Reorder the terms:
-2ab + 3ab + 2a2 + -1a2 = -3ab + a2 + 3ab + -1a2

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

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

Reorder the terms:
1ab + 1a2 = -3ab + 3ab + a2 + -1a2

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

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

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

Simplifying
b + a = 0

Reorder the terms:
a + b = 0

Solving
a + b = 0

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

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

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

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