3a^2+8ab+5b^2=0

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Solution for 3a^2+8ab+5b^2=0 equation: 


Simplifying
3a2 + 8ab + 5b2 = 0

Reorder the terms:
8ab + 3a2 + 5b2 = 0

Solving
8ab + 3a2 + 5b2 = 0

Solving for variable 'a'.

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


Subproblem 1
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

Subproblem 2
Set the factor '(3a + 5b)' equal to zero and attempt to solve:

Simplifying
3a + 5b = 0

Solving
3a + 5b = 0

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

Add '-5b' to each side of the equation.
3a + 5b + -5b = 0 + -5b

Combine like terms: 5b + -5b = 0
3a + 0 = 0 + -5b
3a = 0 + -5b
Remove the zero:
3a = -5b

Divide each side by '3'.
a = -1.666666667b

Simplifying
a = -1.666666667b
Solution
a = {-1b, -1.666666667b}

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