(2y+5)(y+6)=-4(2y+5)

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Solution for (2y+5)(y+6)=-4(2y+5) equation: 


Simplifying
(2y + 5)(y + 6) = -4(2y + 5)

Reorder the terms:
(5 + 2y)(y + 6) = -4(2y + 5)

Reorder the terms:
(5 + 2y)(6 + y) = -4(2y + 5)

Multiply (5 + 2y) * (6 + y)
(5(6 + y) + 2y * (6 + y)) = -4(2y + 5)
((6 * 5 + y * 5) + 2y * (6 + y)) = -4(2y + 5)
((30 + 5y) + 2y * (6 + y)) = -4(2y + 5)
(30 + 5y + (6 * 2y + y * 2y)) = -4(2y + 5)
(30 + 5y + (12y + 2y2)) = -4(2y + 5)

Combine like terms: 5y + 12y = 17y
(30 + 17y + 2y2) = -4(2y + 5)

Reorder the terms:
30 + 17y + 2y2 = -4(5 + 2y)
30 + 17y + 2y2 = (5 * -4 + 2y * -4)
30 + 17y + 2y2 = (-20 + -8y)

Solving
30 + 17y + 2y2 = -20 + -8y

Solving for variable 'y'.

Reorder the terms:
30 + 20 + 17y + 8y + 2y2 = -20 + -8y + 20 + 8y

Combine like terms: 30 + 20 = 50
50 + 17y + 8y + 2y2 = -20 + -8y + 20 + 8y

Combine like terms: 17y + 8y = 25y
50 + 25y + 2y2 = -20 + -8y + 20 + 8y

Reorder the terms:
50 + 25y + 2y2 = -20 + 20 + -8y + 8y

Combine like terms: -20 + 20 = 0
50 + 25y + 2y2 = 0 + -8y + 8y
50 + 25y + 2y2 = -8y + 8y

Combine like terms: -8y + 8y = 0
50 + 25y + 2y2 = 0

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


Subproblem 1
Set the factor '(10 + y)' equal to zero and attempt to solve:

Simplifying
10 + y = 0

Solving
10 + y = 0

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

Add '-10' to each side of the equation.
10 + -10 + y = 0 + -10

Combine like terms: 10 + -10 = 0
0 + y = 0 + -10
y = 0 + -10

Combine like terms: 0 + -10 = -10
y = -10

Simplifying
y = -10

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 = {-10, -2.5}

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