6y^2-2b^2+by=0

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Solution for 6y^2-2b^2+by=0 equation: 


Simplifying
6y2 + -2b2 + by = 0

Reorder the terms:
by + -2b2 + 6y2 = 0

Solving
by + -2b2 + 6y2 = 0

Solving for variable 'b'.

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


Subproblem 1
Set the factor '(-2b + -3y)' equal to zero and attempt to solve:

Simplifying
-2b + -3y = 0

Solving
-2b + -3y = 0

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

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

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

Divide each side by '-2'.
b = -1.5y

Simplifying
b = -1.5y

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

Simplifying
b + -2y = 0

Solving
b + -2y = 0

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

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

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

Simplifying
b = 2y
Solution
b = {-1.5y, 2y}

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