(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 = 4y
(-32 + 4y + 3y2) = 0

Solving
-32 + 4y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-4 + -1y)(8 + -3y) = 0


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 '(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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