(3b+1a)(3b-2a)=0

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Solution for (3b+1a)(3b-2a)=0 equation:


Simplifying
(3b + 1a)(3b + -2a) = 0

Reorder the terms:
(1a + 3b)(3b + -2a) = 0

Reorder the terms:
(1a + 3b)(-2a + 3b) = 0

Multiply (1a + 3b) * (-2a + 3b)
(1a * (-2a + 3b) + 3b * (-2a + 3b)) = 0
((-2a * 1a + 3b * 1a) + 3b * (-2a + 3b)) = 0

Reorder the terms:
((3ab + -2a2) + 3b * (-2a + 3b)) = 0
((3ab + -2a2) + 3b * (-2a + 3b)) = 0
(3ab + -2a2 + (-2a * 3b + 3b * 3b)) = 0
(3ab + -2a2 + (-6ab + 9b2)) = 0

Reorder the terms:
(3ab + -6ab + -2a2 + 9b2) = 0

Combine like terms: 3ab + -6ab = -3ab
(-3ab + -2a2 + 9b2) = 0

Solving
-3ab + -2a2 + 9b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1a + -3b)(2a + -3b) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(2a + -3b)' equal to zero and attempt to solve: Simplifying 2a + -3b = 0 Solving 2a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 2a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 2a + 0 = 0 + 3b 2a = 0 + 3b Remove the zero: 2a = 3b Divide each side by '2'. a = 1.5b Simplifying a = 1.5b

Solution

a = {-3b, 1.5b}

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