3y^2(y+6)-2y(y+6)=

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

Simplifying
3y2(y + 6) + -2y(y + 6) = 0

Reorder the terms:
3y2(6 + y) + -2y(y + 6) = 0
(6 * 3y2 + y * 3y2) + -2y(y + 6) = 0
(18y2 + 3y3) + -2y(y + 6) = 0

Reorder the terms:
18y2 + 3y3 + -2y(6 + y) = 0
18y2 + 3y3 + (6 * -2y + y * -2y) = 0
18y2 + 3y3 + (-12y + -2y2) = 0

Reorder the terms:
-12y + 18y2 + -2y2 + 3y3 = 0

Combine like terms: 18y2 + -2y2 = 16y2
-12y + 16y2 + 3y3 = 0

Solving
-12y + 16y2 + 3y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-12 + 16y + 3y2) = 0

Factor a trinomial.
y((-6 + -1y)(2 + -3y)) = 0

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 '(-6 + -1y)' equal to zero and attempt to solve:

Simplifying
-6 + -1y = 0

Solving
-6 + -1y = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1y = 0 + 6
-1y = 0 + 6

Combine like terms: 0 + 6 = 6
-1y = 6

Divide each side by '-1'.
y = -6

Simplifying
y = -6
Subproblem 3
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
Solution
y = {0, -6, 0.6666666667}