3(y+2)(y-1)=0

Solution for 3(y+2)(y-1)=0 equation:

Simplifying
3(y + 2)(y + -1) = 0

Reorder the terms:
3(2 + y)(y + -1) = 0

Reorder the terms:
3(2 + y)(-1 + y) = 0

Multiply (2 + y) * (-1 + y)
3(2(-1 + y) + y(-1 + y)) = 0
3((-1 * 2 + y * 2) + y(-1 + y)) = 0
3((-2 + 2y) + y(-1 + y)) = 0
3(-2 + 2y + (-1 * y + y * y)) = 0
3(-2 + 2y + (-1y + y2)) = 0

Combine like terms: 2y + -1y = 1y
3(-2 + 1y + y2) = 0
(-2 * 3 + 1y * 3 + y2 * 3) = 0
(-6 + 3y + 3y2) = 0

Solving
-6 + 3y + 3y2 = 0

Solving for variable 'y'.

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

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

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

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 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 + -1y = 0 + 2

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

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

Divide each side by '-1'.
y = -2

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

Simplifying
1 + -1y = 0

Solving
1 + -1y = 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 + -1y = 0 + -1

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

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

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

Simplifying
y = 1
Solution
y = {-2, 1}