6y+9=3(by+3)

Solution for 6y+9=3(by+3) equation:

Simplifying
6y + 9 = 3(by + 3)

Reorder the terms:
9 + 6y = 3(by + 3)

Reorder the terms:
9 + 6y = 3(3 + by)
9 + 6y = (3 * 3 + by * 3)
9 + 6y = (9 + 3by)

Add '-9' to each side of the equation.
9 + -9 + 6y = 9 + -9 + 3by

Combine like terms: 9 + -9 = 0
0 + 6y = 9 + -9 + 3by
6y = 9 + -9 + 3by

Combine like terms: 9 + -9 = 0
6y = 0 + 3by
6y = 3by

Solving
6y = 3by

Solving for variable 'y'.

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

Add '-3by' to each side of the equation.
-3by + 6y = 3by + -3by

Combine like terms: 3by + -3by = 0
-3by + 6y = 0

Factor out the Greatest Common Factor (GCF), '3y'.
3y(-1b + 2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(-1b + 2)' equal to zero and attempt to solve:

Simplifying
-1b + 2 = 0

Reorder the terms:
2 + -1b = 0

Solving
2 + -1b = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1b = 0 + -2
-1b = 0 + -2

Combine like terms: 0 + -2 = -2
-1b = -2

Add 'b' to each side of the equation.
-1b + b = -2 + b

Combine like terms: -1b + b = 0
0 = -2 + b

Simplifying
0 = -2 + b

The solution to this equation could not be determined.

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