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

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


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

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

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

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

Combine like terms: 2y + 30y = 32y
(12 + 32y + 5y2) = -4(5y + 2)

Reorder the terms:
12 + 32y + 5y2 = -4(2 + 5y)
12 + 32y + 5y2 = (2 * -4 + 5y * -4)
12 + 32y + 5y2 = (-8 + -20y)

Solving
12 + 32y + 5y2 = -8 + -20y

Solving for variable 'y'.

Reorder the terms:
12 + 8 + 32y + 20y + 5y2 = -8 + -20y + 8 + 20y

Combine like terms: 12 + 8 = 20
20 + 32y + 20y + 5y2 = -8 + -20y + 8 + 20y

Combine like terms: 32y + 20y = 52y
20 + 52y + 5y2 = -8 + -20y + 8 + 20y

Reorder the terms:
20 + 52y + 5y2 = -8 + 8 + -20y + 20y

Combine like terms: -8 + 8 = 0
20 + 52y + 5y2 = 0 + -20y + 20y
20 + 52y + 5y2 = -20y + 20y

Combine like terms: -20y + 20y = 0
20 + 52y + 5y2 = 0

Factor a trinomial.
(10 + y)(2 + 5y) = 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 '(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 = {-10, -0.4}

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