(3a+2b)(5a+b)=0

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Solution for (3a+2b)(5a+b)=0 equation: 


Simplifying
(3a + 2b)(5a + b) = 0

Multiply (3a + 2b) * (5a + b)
(3a * (5a + b) + 2b * (5a + b)) = 0
((5a * 3a + b * 3a) + 2b * (5a + b)) = 0

Reorder the terms:
((3ab + 15a2) + 2b * (5a + b)) = 0
((3ab + 15a2) + 2b * (5a + b)) = 0
(3ab + 15a2 + (5a * 2b + b * 2b)) = 0
(3ab + 15a2 + (10ab + 2b2)) = 0

Reorder the terms:
(3ab + 10ab + 15a2 + 2b2) = 0

Combine like terms: 3ab + 10ab = 13ab
(13ab + 15a2 + 2b2) = 0

Solving
13ab + 15a2 + 2b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5a + b)(3a + 2b) = 0


Subproblem 1
Set the factor '(5a + b)' equal to zero and attempt to solve:

Simplifying
5a + b = 0

Solving
5a + b = 0

Move all terms containing a to the left, all other terms to the right.

Add '-1b' to each side of the equation.
5a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
5a + 0 = 0 + -1b
5a = 0 + -1b
Remove the zero:
5a = -1b

Divide each side by '5'.
a = -0.2b

Simplifying
a = -0.2b

Subproblem 2
Set the factor '(3a + 2b)' equal to zero and attempt to solve:

Simplifying
3a + 2b = 0

Solving
3a + 2b = 0

Move all terms containing a to the left, all other terms to the right.

Add '-2b' to each side of the equation.
3a + 2b + -2b = 0 + -2b

Combine like terms: 2b + -2b = 0
3a + 0 = 0 + -2b
3a = 0 + -2b
Remove the zero:
3a = -2b

Divide each side by '3'.
a = -0.6666666667b

Simplifying
a = -0.6666666667b
Solution
a = {-0.2b, -0.6666666667b}

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