(2y+5)(y+7)=-5(2y+5)

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Solution for (2y+5)(y+7)=-5(2y+5) equation: 


Simplifying
(2y + 5)(y + 7) = -5(2y + 5)

Reorder the terms:
(5 + 2y)(y + 7) = -5(2y + 5)

Reorder the terms:
(5 + 2y)(7 + y) = -5(2y + 5)

Multiply (5 + 2y) * (7 + y)
(5(7 + y) + 2y * (7 + y)) = -5(2y + 5)
((7 * 5 + y * 5) + 2y * (7 + y)) = -5(2y + 5)
((35 + 5y) + 2y * (7 + y)) = -5(2y + 5)
(35 + 5y + (7 * 2y + y * 2y)) = -5(2y + 5)
(35 + 5y + (14y + 2y2)) = -5(2y + 5)

Combine like terms: 5y + 14y = 19y
(35 + 19y + 2y2) = -5(2y + 5)

Reorder the terms:
35 + 19y + 2y2 = -5(5 + 2y)
35 + 19y + 2y2 = (5 * -5 + 2y * -5)
35 + 19y + 2y2 = (-25 + -10y)

Solving
35 + 19y + 2y2 = -25 + -10y

Solving for variable 'y'.

Reorder the terms:
35 + 25 + 19y + 10y + 2y2 = -25 + -10y + 25 + 10y

Combine like terms: 35 + 25 = 60
60 + 19y + 10y + 2y2 = -25 + -10y + 25 + 10y

Combine like terms: 19y + 10y = 29y
60 + 29y + 2y2 = -25 + -10y + 25 + 10y

Reorder the terms:
60 + 29y + 2y2 = -25 + 25 + -10y + 10y

Combine like terms: -25 + 25 = 0
60 + 29y + 2y2 = 0 + -10y + 10y
60 + 29y + 2y2 = -10y + 10y

Combine like terms: -10y + 10y = 0
60 + 29y + 2y2 = 0

Factor a trinomial.
(12 + y)(5 + 2y) = 0


Subproblem 1
Set the factor '(12 + y)' equal to zero and attempt to solve:

Simplifying
12 + y = 0

Solving
12 + y = 0

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

Add '-12' to each side of the equation.
12 + -12 + y = 0 + -12

Combine like terms: 12 + -12 = 0
0 + y = 0 + -12
y = 0 + -12

Combine like terms: 0 + -12 = -12
y = -12

Simplifying
y = -12

Subproblem 2
Set the factor '(5 + 2y)' equal to zero and attempt to solve:

Simplifying
5 + 2y = 0

Solving
5 + 2y = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2y = 0 + -5
2y = 0 + -5

Combine like terms: 0 + -5 = -5
2y = -5

Divide each side by '2'.
y = -2.5

Simplifying
y = -2.5
Solution
y = {-12, -2.5}

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