2y(y+4)=7(y+4)

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Solution for 2y(y+4)=7(y+4) equation: 


Simplifying
2y(y + 4) = 7(y + 4)

Reorder the terms:
2y(4 + y) = 7(y + 4)
(4 * 2y + y * 2y) = 7(y + 4)
(8y + 2y2) = 7(y + 4)

Reorder the terms:
8y + 2y2 = 7(4 + y)
8y + 2y2 = (4 * 7 + y * 7)
8y + 2y2 = (28 + 7y)

Solving
8y + 2y2 = 28 + 7y

Solving for variable 'y'.

Reorder the terms:
-28 + 8y + -7y + 2y2 = 28 + 7y + -28 + -7y

Combine like terms: 8y + -7y = 1y
-28 + 1y + 2y2 = 28 + 7y + -28 + -7y

Reorder the terms:
-28 + 1y + 2y2 = 28 + -28 + 7y + -7y

Combine like terms: 28 + -28 = 0
-28 + 1y + 2y2 = 0 + 7y + -7y
-28 + 1y + 2y2 = 7y + -7y

Combine like terms: 7y + -7y = 0
-28 + 1y + 2y2 = 0

Factor a trinomial.
(-4 + -1y)(7 + -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 '(7 + -2y)' equal to zero and attempt to solve:

Simplifying
7 + -2y = 0

Solving
7 + -2y = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2y = 0 + -7
-2y = 0 + -7

Combine like terms: 0 + -7 = -7
-2y = -7

Divide each side by '-2'.
y = 3.5

Simplifying
y = 3.5
Solution
y = {-4, 3.5}

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