(3a-b)(a-3b)=

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


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

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

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

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

Combine like terms: -9ab + -1ab = -10ab
(-10ab + 3a2 + 3b2) = 0

Solving
-10ab + 3a2 + 3b2 = 0

Solving for variable 'a'.

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

Subproblem 1

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

Subproblem 2

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

Solution

a = {3b, 0.3333333333b}

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