(y+3)(y+3)-(y+3)(4y)=0

Solution for (y+3)(y+3)-(y+3)(4y)=0 equation:

Simplifying
(y + 3)(y + 3) + -1(y + 3)(4y) = 0

Reorder the terms:
(3 + y)(y + 3) + -1(y + 3)(4y) = 0

Reorder the terms:
(3 + y)(3 + y) + -1(y + 3)(4y) = 0

Multiply (3 + y) * (3 + y)
(3(3 + y) + y(3 + y)) + -1(y + 3)(4y) = 0
((3 * 3 + y * 3) + y(3 + y)) + -1(y + 3)(4y) = 0
((9 + 3y) + y(3 + y)) + -1(y + 3)(4y) = 0
(9 + 3y + (3 * y + y * y)) + -1(y + 3)(4y) = 0
(9 + 3y + (3y + y2)) + -1(y + 3)(4y) = 0

Combine like terms: 3y + 3y = 6y
(9 + 6y + y2) + -1(y + 3)(4y) = 0

Reorder the terms:
9 + 6y + y2 + -1(3 + y)(4y) = 0

Remove parenthesis around (4y)
9 + 6y + y2 + -1(3 + y) * 4y = 0

Reorder the terms for easier multiplication:
9 + 6y + y2 + -1 * 4y(3 + y) = 0

Multiply -1 * 4
9 + 6y + y2 + -4y(3 + y) = 0
9 + 6y + y2 + (3 * -4y + y * -4y) = 0
9 + 6y + y2 + (-12y + -4y2) = 0

Reorder the terms:
9 + 6y + -12y + y2 + -4y2 = 0

Combine like terms: 6y + -12y = -6y
9 + -6y + y2 + -4y2 = 0

Combine like terms: y2 + -4y2 = -3y2
9 + -6y + -3y2 = 0

Solving
9 + -6y + -3y2 = 0

Solving for variable 'y'.

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

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

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

Simplifying
3 + y = 0

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

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

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

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