a(a-2b)+b(2b-a)=0

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Solution for a(a-2b)+b(2b-a)=0 equation:


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

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

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

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

Combine like terms: -2ab + -1ab = -3ab
-3ab + a2 + 2b2 = 0

Solving
-3ab + a2 + 2b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + -2b)(a + -1b) = 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 + -1b)' equal to zero and attempt to solve: Simplifying a + -1b = 0 Solving a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. a + -1b + b = 0 + b Combine like terms: -1b + b = 0 a + 0 = 0 + b a = 0 + b Remove the zero: a = b Simplifying a = b

Solution

a = {2b, b}

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