a(a+b)+b(b+a)=0

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


Simplifying
a(a + b) + b(b + a) = 0
(a * a + b * a) + b(b + a) = 0

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

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

Reorder the terms:
ab + ab + a2 + b2 = 0

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

Solving
2ab + a2 + b2 = 0

Solving for variable 'a'.

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

Subproblem 1

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

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 = {-1b, -1b}

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