(5y+4)(y+5)=-2(5y+4)

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Solution for (5y+4)(y+5)=-2(5y+4) equation: 


Simplifying
(5y + 4)(y + 5) = -2(5y + 4)

Reorder the terms:
(4 + 5y)(y + 5) = -2(5y + 4)

Reorder the terms:
(4 + 5y)(5 + y) = -2(5y + 4)

Multiply (4 + 5y) * (5 + y)
(4(5 + y) + 5y * (5 + y)) = -2(5y + 4)
((5 * 4 + y * 4) + 5y * (5 + y)) = -2(5y + 4)
((20 + 4y) + 5y * (5 + y)) = -2(5y + 4)
(20 + 4y + (5 * 5y + y * 5y)) = -2(5y + 4)
(20 + 4y + (25y + 5y2)) = -2(5y + 4)

Combine like terms: 4y + 25y = 29y
(20 + 29y + 5y2) = -2(5y + 4)

Reorder the terms:
20 + 29y + 5y2 = -2(4 + 5y)
20 + 29y + 5y2 = (4 * -2 + 5y * -2)
20 + 29y + 5y2 = (-8 + -10y)

Solving
20 + 29y + 5y2 = -8 + -10y

Solving for variable 'y'.

Reorder the terms:
20 + 8 + 29y + 10y + 5y2 = -8 + -10y + 8 + 10y

Combine like terms: 20 + 8 = 28
28 + 29y + 10y + 5y2 = -8 + -10y + 8 + 10y

Combine like terms: 29y + 10y = 39y
28 + 39y + 5y2 = -8 + -10y + 8 + 10y

Reorder the terms:
28 + 39y + 5y2 = -8 + 8 + -10y + 10y

Combine like terms: -8 + 8 = 0
28 + 39y + 5y2 = 0 + -10y + 10y
28 + 39y + 5y2 = -10y + 10y

Combine like terms: -10y + 10y = 0
28 + 39y + 5y2 = 0

Factor a trinomial.
(7 + y)(4 + 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 '(4 + 5y)' equal to zero and attempt to solve:

Simplifying
4 + 5y = 0

Solving
4 + 5y = 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 + 5y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5y = 0 + -4
5y = 0 + -4

Combine like terms: 0 + -4 = -4
5y = -4

Divide each side by '5'.
y = -0.8

Simplifying
y = -0.8
Solution
y = {-7, -0.8}

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