y(y+6)(12)-(y+6)(y-6)2=y(16y+6)

Solution for y(y+6)(12)-(y+6)(y-6)2=y(16y+6) equation:

Simplifying
y(y + 6)(12) + -1(y + 6)(y + -6) * 2 = y(16y + 6)

Reorder the terms:
y(6 + y)(12) + -1(y + 6)(y + -6) * 2 = y(16y + 6)

Reorder the terms for easier multiplication:
12y(6 + y) + -1(y + 6)(y + -6) * 2 = y(16y + 6)
(6 * 12y + y * 12y) + -1(y + 6)(y + -6) * 2 = y(16y + 6)
(72y + 12y2) + -1(y + 6)(y + -6) * 2 = y(16y + 6)

Reorder the terms:
72y + 12y2 + -1(6 + y)(y + -6) * 2 = y(16y + 6)

Reorder the terms:
72y + 12y2 + -1(6 + y)(-6 + y) * 2 = y(16y + 6)

Reorder the terms for easier multiplication:
72y + 12y2 + -1 * 2(6 + y)(-6 + y) = y(16y + 6)

Multiply -1 * 2
72y + 12y2 + -2(6 + y)(-6 + y) = y(16y + 6)

Multiply (6 + y) * (-6 + y)
72y + 12y2 + -2(6(-6 + y) + y(-6 + y)) = y(16y + 6)
72y + 12y2 + -2((-6 * 6 + y * 6) + y(-6 + y)) = y(16y + 6)
72y + 12y2 + -2((-36 + 6y) + y(-6 + y)) = y(16y + 6)
72y + 12y2 + -2(-36 + 6y + (-6 * y + y * y)) = y(16y + 6)
72y + 12y2 + -2(-36 + 6y + (-6y + y2)) = y(16y + 6)

Combine like terms: 6y + -6y = 0
72y + 12y2 + -2(-36 + 0 + y2) = y(16y + 6)
72y + 12y2 + -2(-36 + y2) = y(16y + 6)
72y + 12y2 + (-36 * -2 + y2 * -2) = y(16y + 6)
72y + 12y2 + (72 + -2y2) = y(16y + 6)

Reorder the terms:
72 + 72y + 12y2 + -2y2 = y(16y + 6)

Combine like terms: 12y2 + -2y2 = 10y2
72 + 72y + 10y2 = y(16y + 6)

Reorder the terms:
72 + 72y + 10y2 = y(6 + 16y)
72 + 72y + 10y2 = (6 * y + 16y * y)
72 + 72y + 10y2 = (6y + 16y2)

Solving
72 + 72y + 10y2 = 6y + 16y2

Solving for variable 'y'.

Reorder the terms:
72 + 72y + -6y + 10y2 + -16y2 = 6y + 16y2 + -6y + -16y2

Combine like terms: 72y + -6y = 66y
72 + 66y + 10y2 + -16y2 = 6y + 16y2 + -6y + -16y2

Combine like terms: 10y2 + -16y2 = -6y2
72 + 66y + -6y2 = 6y + 16y2 + -6y + -16y2

Reorder the terms:
72 + 66y + -6y2 = 6y + -6y + 16y2 + -16y2

Combine like terms: 6y + -6y = 0
72 + 66y + -6y2 = 0 + 16y2 + -16y2
72 + 66y + -6y2 = 16y2 + -16y2

Combine like terms: 16y2 + -16y2 = 0
72 + 66y + -6y2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(12 + 11y + -1y2) = 0

Factor a trinomial.
6((12 + -1y)(1 + y)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(12 + -1y)' equal to zero and attempt to solve:

Simplifying
12 + -1y = 0

Solving
12 + -1y = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1y = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1y = 0 + -12
-1y = 0 + -12

Combine like terms: 0 + -12 = -12
-1y = -12

Divide each side by '-1'.
y = 12

Simplifying
y = 12
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 = {12, -1}