(3y+8)(4+y)=0

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Solution for (3y+8)(4+y)=0 equation: 


Simplifying
(3y + 8)(4 + y) = 0

Reorder the terms:
(8 + 3y)(4 + y) = 0

Multiply (8 + 3y) * (4 + y)
(8(4 + y) + 3y * (4 + y)) = 0
((4 * 8 + y * 8) + 3y * (4 + y)) = 0
((32 + 8y) + 3y * (4 + y)) = 0
(32 + 8y + (4 * 3y + y * 3y)) = 0
(32 + 8y + (12y + 3y2)) = 0

Combine like terms: 8y + 12y = 20y
(32 + 20y + 3y2) = 0

Solving
32 + 20y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(4 + y)(8 + 3y) = 0


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

Simplifying
4 + y = 0

Solving
4 + y = 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 + y = 0 + -4

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

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

Simplifying
y = -4

Subproblem 2
Set the factor '(8 + 3y)' equal to zero and attempt to solve:

Simplifying
8 + 3y = 0

Solving
8 + 3y = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3y = 0 + -8
3y = 0 + -8

Combine like terms: 0 + -8 = -8
3y = -8

Divide each side by '3'.
y = -2.666666667

Simplifying
y = -2.666666667
Solution
y = {-4, -2.666666667}

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