a*(a-2b)-b*(2b-a)=

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


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

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

Reorder the terms:
-2ab + a2 + -1b(-1a + 2b) = 0
-2ab + a2 + (-1a * -1b + 2b * -1b) = 0
-2ab + a2 + (1ab + -2b2) = 0

Reorder the terms:
-2ab + 1ab + a2 + -2b2 = 0

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

Solving
-1ab + a2 + -2b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + -2b)(a + b) = 0


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

Simplifying
a + -2b = 0

Solving
a + -2b = 0

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

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

Combine like terms: -2b + 2b = 0
a + 0 = 0 + 2b
a = 0 + 2b
Remove the zero:
a = 2b

Simplifying
a = 2b

Subproblem 2
Set the factor '(a + b)' equal to zero and attempt to solve:

Simplifying
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 = {2b, -1b}

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