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

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

Simplifying
6y + -2(y + 1) * 3(y + -2) + 6 = 0

Reorder the terms:
6y + -2(1 + y) * 3(y + -2) + 6 = 0

Reorder the terms:
6y + -2(1 + y) * 3(-2 + y) + 6 = 0

Reorder the terms for easier multiplication:
6y + -2 * 3(1 + y)(-2 + y) + 6 = 0

Multiply -2 * 3
6y + -6(1 + y)(-2 + y) + 6 = 0

Multiply (1 + y) * (-2 + y)
6y + -6(1(-2 + y) + y(-2 + y)) + 6 = 0
6y + -6((-2 * 1 + y * 1) + y(-2 + y)) + 6 = 0
6y + -6((-2 + 1y) + y(-2 + y)) + 6 = 0
6y + -6(-2 + 1y + (-2 * y + y * y)) + 6 = 0
6y + -6(-2 + 1y + (-2y + y2)) + 6 = 0

Combine like terms: 1y + -2y = -1y
6y + -6(-2 + -1y + y2) + 6 = 0
6y + (-2 * -6 + -1y * -6 + y2 * -6) + 6 = 0
6y + (12 + 6y + -6y2) + 6 = 0

Reorder the terms:
12 + 6 + 6y + 6y + -6y2 = 0

Combine like terms: 12 + 6 = 18
18 + 6y + 6y + -6y2 = 0

Combine like terms: 6y + 6y = 12y
18 + 12y + -6y2 = 0

Solving
18 + 12y + -6y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + 2y + -1y2) = 0

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

Ignore the factor 6.
Subproblem 1
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

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

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Subproblem 2
Set the factor '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

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

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

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

Simplifying
y = -1
Solution
y = {3, -1}