2(y+3)y=8

Solution for 2(y+3)y=8 equation:

Simplifying
2(y + 3) * y = 8

Reorder the terms:
2(3 + y) * y = 8

Reorder the terms for easier multiplication:
2y(3 + y) = 8
(3 * 2y + y * 2y) = 8
(6y + 2y2) = 8

Solving
6y + 2y2 = 8

Solving for variable 'y'.

Reorder the terms:
-8 + 6y + 2y2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 6y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 3y + y2) = 0

Factor a trinomial.
2((-4 + -1y)(1 + -1y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -1y)' equal to zero and attempt to solve:

Simplifying
-4 + -1y = 0

Solving
-4 + -1y = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1y = 0 + 4
-1y = 0 + 4

Combine like terms: 0 + 4 = 4
-1y = 4

Divide each side by '-1'.
y = -4

Simplifying
y = -4
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 = {-4, 1}