3b(y+by+1)=2b(2-y+2b)

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Solution for 3b(y+by+1)=2b(2-y+2b) equation: 


Simplifying
3b(y + by + 1) = 2b(2 + -1y + 2b)

Reorder the terms:
3b(1 + by + y) = 2b(2 + -1y + 2b)
(1 * 3b + by * 3b + y * 3b) = 2b(2 + -1y + 2b)

Reorder the terms:
(3b + 3by + 3b2y) = 2b(2 + -1y + 2b)
(3b + 3by + 3b2y) = 2b(2 + -1y + 2b)

Reorder the terms:
3b + 3by + 3b2y = 2b(2 + 2b + -1y)
3b + 3by + 3b2y = (2 * 2b + 2b * 2b + -1y * 2b)

Reorder the terms:
3b + 3by + 3b2y = (4b + -2by + 4b2)
3b + 3by + 3b2y = (4b + -2by + 4b2)

Solving
3b + 3by + 3b2y = 4b + -2by + 4b2

Solving for variable 'b'.

Reorder the terms:
3b + -4b + 3by + 2by + -4b2 + 3b2y = 4b + -2by + 4b2 + -4b + 2by + -4b2

Combine like terms: 3b + -4b = -1b
-1b + 3by + 2by + -4b2 + 3b2y = 4b + -2by + 4b2 + -4b + 2by + -4b2

Combine like terms: 3by + 2by = 5by
-1b + 5by + -4b2 + 3b2y = 4b + -2by + 4b2 + -4b + 2by + -4b2

Reorder the terms:
-1b + 5by + -4b2 + 3b2y = 4b + -4b + -2by + 2by + 4b2 + -4b2

Combine like terms: 4b + -4b = 0
-1b + 5by + -4b2 + 3b2y = 0 + -2by + 2by + 4b2 + -4b2
-1b + 5by + -4b2 + 3b2y = -2by + 2by + 4b2 + -4b2

Combine like terms: -2by + 2by = 0
-1b + 5by + -4b2 + 3b2y = 0 + 4b2 + -4b2
-1b + 5by + -4b2 + 3b2y = 4b2 + -4b2

Combine like terms: 4b2 + -4b2 = 0
-1b + 5by + -4b2 + 3b2y = 0

Factor out the Greatest Common Factor (GCF), 'b'.
b(-1 + 5y + -4b + 3by) = 0


Subproblem 1
Set the factor 'b' equal to zero and attempt to solve:

Simplifying
b = 0

Solving
b = 0

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

Simplifying
b = 0

Subproblem 2
Set the factor '(-1 + 5y + -4b + 3by)' equal to zero and attempt to solve:

Simplifying
-1 + 5y + -4b + 3by = 0

Reorder the terms:
-1 + -4b + 3by + 5y = 0

Solving
-1 + -4b + 3by + 5y = 0

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

Add '1' to each side of the equation.
-1 + -4b + 3by + 1 + 5y = 0 + 1

Reorder the terms:
-1 + 1 + -4b + 3by + 5y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4b + 3by + 5y = 0 + 1
-4b + 3by + 5y = 0 + 1

Combine like terms: 0 + 1 = 1
-4b + 3by + 5y = 1

Add '-5y' to each side of the equation.
-4b + 3by + 5y + -5y = 1 + -5y

Combine like terms: 5y + -5y = 0
-4b + 3by + 0 = 1 + -5y
-4b + 3by = 1 + -5y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
b = {0}

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