3(y-2)=6(y-1)3y

Solution for 3(y-2)=6(y-1)3y equation:

Simplifying
3(y + -2) = 6(y + -1) * 3y

Reorder the terms:
3(-2 + y) = 6(y + -1) * 3y
(-2 * 3 + y * 3) = 6(y + -1) * 3y
(-6 + 3y) = 6(y + -1) * 3y

Reorder the terms:
-6 + 3y = 6(-1 + y) * 3y

Reorder the terms for easier multiplication:
-6 + 3y = 6 * 3y(-1 + y)

Multiply 6 * 3
-6 + 3y = 18y(-1 + y)
-6 + 3y = (-1 * 18y + y * 18y)
-6 + 3y = (-18y + 18y2)

Solving
-6 + 3y = -18y + 18y2

Solving for variable 'y'.

Combine like terms: 3y + 18y = 21y
-6 + 21y + -18y2 = -18y + 18y2 + 18y + -18y2

Reorder the terms:
-6 + 21y + -18y2 = -18y + 18y + 18y2 + -18y2

Combine like terms: -18y + 18y = 0
-6 + 21y + -18y2 = 0 + 18y2 + -18y2
-6 + 21y + -18y2 = 18y2 + -18y2

Combine like terms: 18y2 + -18y2 = 0
-6 + 21y + -18y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 7y + -6y2) = 0

Factor a trinomial.
3((-2 + 3y)(1 + -2y)) = 0

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

Simplifying
-2 + 3y = 0

Solving
-2 + 3y = 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 + 3y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3y = 0 + 2
3y = 0 + 2

Combine like terms: 0 + 2 = 2
3y = 2

Divide each side by '3'.
y = 0.6666666667

Simplifying
y = 0.6666666667
Subproblem 2
Set the factor '(1 + -2y)' equal to zero and attempt to solve:

Simplifying
1 + -2y = 0

Solving
1 + -2y = 0

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

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

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

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

Divide each side by '-2'.
y = 0.5

Simplifying
y = 0.5
Solution
y = {0.6666666667, 0.5}