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

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


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

Reorder the terms:
2y(4 + y) = 3(y + 4)
(4 * 2y + y * 2y) = 3(y + 4)
(8y + 2y2) = 3(y + 4)

Reorder the terms:
8y + 2y2 = 3(4 + y)
8y + 2y2 = (4 * 3 + y * 3)
8y + 2y2 = (12 + 3y)

Solving
8y + 2y2 = 12 + 3y

Solving for variable 'y'.

Reorder the terms:
-12 + 8y + -3y + 2y2 = 12 + 3y + -12 + -3y

Combine like terms: 8y + -3y = 5y
-12 + 5y + 2y2 = 12 + 3y + -12 + -3y

Reorder the terms:
-12 + 5y + 2y2 = 12 + -12 + 3y + -3y

Combine like terms: 12 + -12 = 0
-12 + 5y + 2y2 = 0 + 3y + -3y
-12 + 5y + 2y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
-12 + 5y + 2y2 = 0

Factor a trinomial.
(-4 + -1y)(3 + -2y) = 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 '(3 + -2y)' equal to zero and attempt to solve:

Simplifying
3 + -2y = 0

Solving
3 + -2y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2y = 0 + -3
-2y = 0 + -3

Combine like terms: 0 + -3 = -3
-2y = -3

Divide each side by '-2'.
y = 1.5

Simplifying
y = 1.5
Solution
y = {-4, 1.5}

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