(a+b)(3a+b)=0

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Solution for (a+b)(3a+b)=0 equation:


Simplifying
(a + b)(3a + b) = 0

Multiply (a + b) * (3a + b)
(a(3a + b) + b(3a + b)) = 0
((3a * a + b * a) + b(3a + b)) = 0

Reorder the terms:
((ab + 3a2) + b(3a + b)) = 0
((ab + 3a2) + b(3a + b)) = 0
(ab + 3a2 + (3a * b + b * b)) = 0
(ab + 3a2 + (3ab + b2)) = 0

Reorder the terms:
(ab + 3ab + 3a2 + b2) = 0

Combine like terms: ab + 3ab = 4ab
(4ab + 3a2 + b2) = 0

Solving
4ab + 3a2 + b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3a + b)(a + b) = 0

Subproblem 1

Set the factor '(3a + b)' equal to zero and attempt to solve: Simplifying 3a + b = 0 Solving 3a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 3a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 3a + 0 = 0 + -1b 3a = 0 + -1b Remove the zero: 3a = -1b Divide each side by '3'. a = -0.3333333333b Simplifying a = -0.3333333333b

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 = {-0.3333333333b, -1b}

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