(5y+4)(y+7)=-3(5y+4)

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Solution for (5y+4)(y+7)=-3(5y+4) equation: 


Simplifying
(5y + 4)(y + 7) = -3(5y + 4)

Reorder the terms:
(4 + 5y)(y + 7) = -3(5y + 4)

Reorder the terms:
(4 + 5y)(7 + y) = -3(5y + 4)

Multiply (4 + 5y) * (7 + y)
(4(7 + y) + 5y * (7 + y)) = -3(5y + 4)
((7 * 4 + y * 4) + 5y * (7 + y)) = -3(5y + 4)
((28 + 4y) + 5y * (7 + y)) = -3(5y + 4)
(28 + 4y + (7 * 5y + y * 5y)) = -3(5y + 4)
(28 + 4y + (35y + 5y2)) = -3(5y + 4)

Combine like terms: 4y + 35y = 39y
(28 + 39y + 5y2) = -3(5y + 4)

Reorder the terms:
28 + 39y + 5y2 = -3(4 + 5y)
28 + 39y + 5y2 = (4 * -3 + 5y * -3)
28 + 39y + 5y2 = (-12 + -15y)

Solving
28 + 39y + 5y2 = -12 + -15y

Solving for variable 'y'.

Reorder the terms:
28 + 12 + 39y + 15y + 5y2 = -12 + -15y + 12 + 15y

Combine like terms: 28 + 12 = 40
40 + 39y + 15y + 5y2 = -12 + -15y + 12 + 15y

Combine like terms: 39y + 15y = 54y
40 + 54y + 5y2 = -12 + -15y + 12 + 15y

Reorder the terms:
40 + 54y + 5y2 = -12 + 12 + -15y + 15y

Combine like terms: -12 + 12 = 0
40 + 54y + 5y2 = 0 + -15y + 15y
40 + 54y + 5y2 = -15y + 15y

Combine like terms: -15y + 15y = 0
40 + 54y + 5y2 = 0

Factor a trinomial.
(10 + y)(4 + 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 '(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 = {-10, -0.8}

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