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

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


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

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

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

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

Combine like terms: 2y + 35y = 37y
(14 + 37y + 5y2) = -2(5y + 2)

Reorder the terms:
14 + 37y + 5y2 = -2(2 + 5y)
14 + 37y + 5y2 = (2 * -2 + 5y * -2)
14 + 37y + 5y2 = (-4 + -10y)

Solving
14 + 37y + 5y2 = -4 + -10y

Solving for variable 'y'.

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

Combine like terms: 14 + 4 = 18
18 + 37y + 10y + 5y2 = -4 + -10y + 4 + 10y

Combine like terms: 37y + 10y = 47y
18 + 47y + 5y2 = -4 + -10y + 4 + 10y

Reorder the terms:
18 + 47y + 5y2 = -4 + 4 + -10y + 10y

Combine like terms: -4 + 4 = 0
18 + 47y + 5y2 = 0 + -10y + 10y
18 + 47y + 5y2 = -10y + 10y

Combine like terms: -10y + 10y = 0
18 + 47y + 5y2 = 0

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


Subproblem 1
Set the factor '(9 + y)' equal to zero and attempt to solve:

Simplifying
9 + y = 0

Solving
9 + y = 0

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

Add '-9' to each side of the equation.
9 + -9 + y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + y = 0 + -9
y = 0 + -9

Combine like terms: 0 + -9 = -9
y = -9

Simplifying
y = -9

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 = {-9, -0.4}

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