(3y-2)(y+4)=24

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Solution for (3y-2)(y+4)=24 equation: 


Simplifying
(3y + -2)(y + 4) = 24

Reorder the terms:
(-2 + 3y)(y + 4) = 24

Reorder the terms:
(-2 + 3y)(4 + y) = 24

Multiply (-2 + 3y) * (4 + y)
(-2(4 + y) + 3y * (4 + y)) = 24
((4 * -2 + y * -2) + 3y * (4 + y)) = 24
((-8 + -2y) + 3y * (4 + y)) = 24
(-8 + -2y + (4 * 3y + y * 3y)) = 24
(-8 + -2y + (12y + 3y2)) = 24

Combine like terms: -2y + 12y = 10y
(-8 + 10y + 3y2) = 24

Solving
-8 + 10y + 3y2 = 24

Solving for variable 'y'.

Reorder the terms:
-8 + -24 + 10y + 3y2 = 24 + -24

Combine like terms: -8 + -24 = -32
-32 + 10y + 3y2 = 24 + -24

Combine like terms: 24 + -24 = 0
-32 + 10y + 3y2 = 0

Factor a trinomial.
(-16 + -3y)(2 + -1y) = 0


Subproblem 1
Set the factor '(-16 + -3y)' equal to zero and attempt to solve:

Simplifying
-16 + -3y = 0

Solving
-16 + -3y = 0

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

Add '16' to each side of the equation.
-16 + 16 + -3y = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -3y = 0 + 16
-3y = 0 + 16

Combine like terms: 0 + 16 = 16
-3y = 16

Divide each side by '-3'.
y = -5.333333333

Simplifying
y = -5.333333333

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

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {-5.333333333, 2}

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