(5y+2)(y+2)=-3(5y+2)

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Solution for (5y+2)(y+2)=-3(5y+2) equation: 


Simplifying
(5y + 2)(y + 2) = -3(5y + 2)

Reorder the terms:
(2 + 5y)(y + 2) = -3(5y + 2)

Reorder the terms:
(2 + 5y)(2 + y) = -3(5y + 2)

Multiply (2 + 5y) * (2 + y)
(2(2 + y) + 5y * (2 + y)) = -3(5y + 2)
((2 * 2 + y * 2) + 5y * (2 + y)) = -3(5y + 2)
((4 + 2y) + 5y * (2 + y)) = -3(5y + 2)
(4 + 2y + (2 * 5y + y * 5y)) = -3(5y + 2)
(4 + 2y + (10y + 5y2)) = -3(5y + 2)

Combine like terms: 2y + 10y = 12y
(4 + 12y + 5y2) = -3(5y + 2)

Reorder the terms:
4 + 12y + 5y2 = -3(2 + 5y)
4 + 12y + 5y2 = (2 * -3 + 5y * -3)
4 + 12y + 5y2 = (-6 + -15y)

Solving
4 + 12y + 5y2 = -6 + -15y

Solving for variable 'y'.

Reorder the terms:
4 + 6 + 12y + 15y + 5y2 = -6 + -15y + 6 + 15y

Combine like terms: 4 + 6 = 10
10 + 12y + 15y + 5y2 = -6 + -15y + 6 + 15y

Combine like terms: 12y + 15y = 27y
10 + 27y + 5y2 = -6 + -15y + 6 + 15y

Reorder the terms:
10 + 27y + 5y2 = -6 + 6 + -15y + 15y

Combine like terms: -6 + 6 = 0
10 + 27y + 5y2 = 0 + -15y + 15y
10 + 27y + 5y2 = -15y + 15y

Combine like terms: -15y + 15y = 0
10 + 27y + 5y2 = 0

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


Subproblem 1
Set the factor '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

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

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

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

Simplifying
y = -5

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 = {-5, -0.4}

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