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

Solution for (4(y-2)(y+6))+(2(y+3)(y+6))=(6(y+3)(y-2)) equation:

Simplifying
(4(y + -2)(y + 6)) + (2(y + 3)(y + 6)) = (6(y + 3)(y + -2))

Reorder the terms:
(4(-2 + y)(y + 6)) + (2(y + 3)(y + 6)) = (6(y + 3)(y + -2))

Reorder the terms:
(4(-2 + y)(6 + y)) + (2(y + 3)(y + 6)) = (6(y + 3)(y + -2))

Multiply (-2 + y) * (6 + y)
(4(-2(6 + y) + y(6 + y))) + (2(y + 3)(y + 6)) = (6(y + 3)(y + -2))
(4((6 * -2 + y * -2) + y(6 + y))) + (2(y + 3)(y + 6)) = (6(y + 3)(y + -2))
(4((-12 + -2y) + y(6 + y))) + (2(y + 3)(y + 6)) = (6(y + 3)(y + -2))
(4(-12 + -2y + (6 * y + y * y))) + (2(y + 3)(y + 6)) = (6(y + 3)(y + -2))
(4(-12 + -2y + (6y + y2))) + (2(y + 3)(y + 6)) = (6(y + 3)(y + -2))

Combine like terms: -2y + 6y = 4y
(4(-12 + 4y + y2)) + (2(y + 3)(y + 6)) = (6(y + 3)(y + -2))
((-12 * 4 + 4y * 4 + y2 * 4)) + (2(y + 3)(y + 6)) = (6(y + 3)(y + -2))
((-48 + 16y + 4y2)) + (2(y + 3)(y + 6)) = (6(y + 3)(y + -2))
(-48 + 16y + 4y2) + (2(y + 3)(y + 6)) = (6(y + 3)(y + -2))

Remove parenthesis around (-48 + 16y + 4y2)
-48 + 16y + 4y2 + (2(y + 3)(y + 6)) = (6(y + 3)(y + -2))

Reorder the terms:
-48 + 16y + 4y2 + (2(3 + y)(y + 6)) = (6(y + 3)(y + -2))

Reorder the terms:
-48 + 16y + 4y2 + (2(3 + y)(6 + y)) = (6(y + 3)(y + -2))

Multiply (3 + y) * (6 + y)
-48 + 16y + 4y2 + (2(3(6 + y) + y(6 + y))) = (6(y + 3)(y + -2))
-48 + 16y + 4y2 + (2((6 * 3 + y * 3) + y(6 + y))) = (6(y + 3)(y + -2))
-48 + 16y + 4y2 + (2((18 + 3y) + y(6 + y))) = (6(y + 3)(y + -2))
-48 + 16y + 4y2 + (2(18 + 3y + (6 * y + y * y))) = (6(y + 3)(y + -2))
-48 + 16y + 4y2 + (2(18 + 3y + (6y + y2))) = (6(y + 3)(y + -2))

Combine like terms: 3y + 6y = 9y
-48 + 16y + 4y2 + (2(18 + 9y + y2)) = (6(y + 3)(y + -2))
-48 + 16y + 4y2 + ((18 * 2 + 9y * 2 + y2 * 2)) = (6(y + 3)(y + -2))
-48 + 16y + 4y2 + ((36 + 18y + 2y2)) = (6(y + 3)(y + -2))
-48 + 16y + 4y2 + (36 + 18y + 2y2) = (6(y + 3)(y + -2))

Remove parenthesis around (36 + 18y + 2y2)
-48 + 16y + 4y2 + 36 + 18y + 2y2 = (6(y + 3)(y + -2))

Reorder the terms:
-48 + 36 + 16y + 18y + 4y2 + 2y2 = (6(y + 3)(y + -2))

Combine like terms: -48 + 36 = -12
-12 + 16y + 18y + 4y2 + 2y2 = (6(y + 3)(y + -2))

Combine like terms: 16y + 18y = 34y
-12 + 34y + 4y2 + 2y2 = (6(y + 3)(y + -2))

Combine like terms: 4y2 + 2y2 = 6y2
-12 + 34y + 6y2 = (6(y + 3)(y + -2))

Reorder the terms:
-12 + 34y + 6y2 = (6(3 + y)(y + -2))

Reorder the terms:
-12 + 34y + 6y2 = (6(3 + y)(-2 + y))

Multiply (3 + y) * (-2 + y)
-12 + 34y + 6y2 = (6(3(-2 + y) + y(-2 + y)))
-12 + 34y + 6y2 = (6((-2 * 3 + y * 3) + y(-2 + y)))
-12 + 34y + 6y2 = (6((-6 + 3y) + y(-2 + y)))
-12 + 34y + 6y2 = (6(-6 + 3y + (-2 * y + y * y)))
-12 + 34y + 6y2 = (6(-6 + 3y + (-2y + y2)))

Combine like terms: 3y + -2y = 1y
-12 + 34y + 6y2 = (6(-6 + 1y + y2))
-12 + 34y + 6y2 = ((-6 * 6 + 1y * 6 + y2 * 6))
-12 + 34y + 6y2 = ((-36 + 6y + 6y2))
-12 + 34y + 6y2 = (-36 + 6y + 6y2)

Remove parenthesis around (-36 + 6y + 6y2)
-12 + 34y + 6y2 = -36 + 6y + 6y2

Add '-6y2' to each side of the equation.
-12 + 34y + 6y2 + -6y2 = -36 + 6y + 6y2 + -6y2

Combine like terms: 6y2 + -6y2 = 0
-12 + 34y + 0 = -36 + 6y + 6y2 + -6y2
-12 + 34y = -36 + 6y + 6y2 + -6y2

Combine like terms: 6y2 + -6y2 = 0
-12 + 34y = -36 + 6y + 0
-12 + 34y = -36 + 6y

Solving
-12 + 34y = -36 + 6y

Solving for variable 'y'.

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

Add '-6y' to each side of the equation.
-12 + 34y + -6y = -36 + 6y + -6y

Combine like terms: 34y + -6y = 28y
-12 + 28y = -36 + 6y + -6y

Combine like terms: 6y + -6y = 0
-12 + 28y = -36 + 0
-12 + 28y = -36

Add '12' to each side of the equation.
-12 + 12 + 28y = -36 + 12

Combine like terms: -12 + 12 = 0
0 + 28y = -36 + 12
28y = -36 + 12

Combine like terms: -36 + 12 = -24
28y = -24

Divide each side by '28'.
y = -0.8571428571

Simplifying
y = -0.8571428571