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

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


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

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

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

Multiply (2 + 5y) * (5 + y)
(2(5 + y) + 5y * (5 + y)) = -2(5y + 2)
((5 * 2 + y * 2) + 5y * (5 + y)) = -2(5y + 2)
((10 + 2y) + 5y * (5 + y)) = -2(5y + 2)
(10 + 2y + (5 * 5y + y * 5y)) = -2(5y + 2)
(10 + 2y + (25y + 5y2)) = -2(5y + 2)

Combine like terms: 2y + 25y = 27y
(10 + 27y + 5y2) = -2(5y + 2)

Reorder the terms:
10 + 27y + 5y2 = -2(2 + 5y)
10 + 27y + 5y2 = (2 * -2 + 5y * -2)
10 + 27y + 5y2 = (-4 + -10y)

Solving
10 + 27y + 5y2 = -4 + -10y

Solving for variable 'y'.

Reorder the terms:
10 + 4 + 27y + 10y + 5y2 = -4 + -10y + 4 + 10y

Combine like terms: 10 + 4 = 14
14 + 27y + 10y + 5y2 = -4 + -10y + 4 + 10y

Combine like terms: 27y + 10y = 37y
14 + 37y + 5y2 = -4 + -10y + 4 + 10y

Reorder the terms:
14 + 37y + 5y2 = -4 + 4 + -10y + 10y

Combine like terms: -4 + 4 = 0
14 + 37y + 5y2 = 0 + -10y + 10y
14 + 37y + 5y2 = -10y + 10y

Combine like terms: -10y + 10y = 0
14 + 37y + 5y2 = 0

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


Subproblem 1
Set the factor '(7 + y)' equal to zero and attempt to solve:

Simplifying
7 + y = 0

Solving
7 + y = 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 + y = 0 + -7

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

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

Simplifying
y = -7

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

Simplifying
2 + 5y = 0

Solving
2 + 5y = 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 + 5y = 0 + -2

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

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

Divide each side by '5'.
y = -0.4

Simplifying
y = -0.4
Solution
y = {-7, -0.4}

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