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

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


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

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

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

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

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

Reorder the terms:
14 + 37y + 5y2 = -5(2 + 5y)
14 + 37y + 5y2 = (2 * -5 + 5y * -5)
14 + 37y + 5y2 = (-10 + -25y)

Solving
14 + 37y + 5y2 = -10 + -25y

Solving for variable 'y'.

Reorder the terms:
14 + 10 + 37y + 25y + 5y2 = -10 + -25y + 10 + 25y

Combine like terms: 14 + 10 = 24
24 + 37y + 25y + 5y2 = -10 + -25y + 10 + 25y

Combine like terms: 37y + 25y = 62y
24 + 62y + 5y2 = -10 + -25y + 10 + 25y

Reorder the terms:
24 + 62y + 5y2 = -10 + 10 + -25y + 25y

Combine like terms: -10 + 10 = 0
24 + 62y + 5y2 = 0 + -25y + 25y
24 + 62y + 5y2 = -25y + 25y

Combine like terms: -25y + 25y = 0
24 + 62y + 5y2 = 0

Factor a trinomial.
(12 + y)(2 + 5y) = 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 '(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 = {-12, -0.4}

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