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

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


Simplifying
(a + 3b)(3a + -1b) = 0

Multiply (a + 3b) * (3a + -1b)
(a(3a + -1b) + 3b * (3a + -1b)) = 0
((3a * a + -1b * a) + 3b * (3a + -1b)) = 0

Reorder the terms:
((-1ab + 3a2) + 3b * (3a + -1b)) = 0
((-1ab + 3a2) + 3b * (3a + -1b)) = 0
(-1ab + 3a2 + (3a * 3b + -1b * 3b)) = 0
(-1ab + 3a2 + (9ab + -3b2)) = 0

Reorder the terms:
(-1ab + 9ab + 3a2 + -3b2) = 0

Combine like terms: -1ab + 9ab = 8ab
(8ab + 3a2 + -3b2) = 0

Solving
8ab + 3a2 + -3b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3a + -1b)(a + 3b) = 0

Subproblem 1

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

Subproblem 2

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

Solution

a = {0.3333333333b, -3b}

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