(4y+3)(y+7)=-2(4y+3)

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Solution for (4y+3)(y+7)=-2(4y+3) equation: 


Simplifying
(4y + 3)(y + 7) = -2(4y + 3)

Reorder the terms:
(3 + 4y)(y + 7) = -2(4y + 3)

Reorder the terms:
(3 + 4y)(7 + y) = -2(4y + 3)

Multiply (3 + 4y) * (7 + y)
(3(7 + y) + 4y * (7 + y)) = -2(4y + 3)
((7 * 3 + y * 3) + 4y * (7 + y)) = -2(4y + 3)
((21 + 3y) + 4y * (7 + y)) = -2(4y + 3)
(21 + 3y + (7 * 4y + y * 4y)) = -2(4y + 3)
(21 + 3y + (28y + 4y2)) = -2(4y + 3)

Combine like terms: 3y + 28y = 31y
(21 + 31y + 4y2) = -2(4y + 3)

Reorder the terms:
21 + 31y + 4y2 = -2(3 + 4y)
21 + 31y + 4y2 = (3 * -2 + 4y * -2)
21 + 31y + 4y2 = (-6 + -8y)

Solving
21 + 31y + 4y2 = -6 + -8y

Solving for variable 'y'.

Reorder the terms:
21 + 6 + 31y + 8y + 4y2 = -6 + -8y + 6 + 8y

Combine like terms: 21 + 6 = 27
27 + 31y + 8y + 4y2 = -6 + -8y + 6 + 8y

Combine like terms: 31y + 8y = 39y
27 + 39y + 4y2 = -6 + -8y + 6 + 8y

Reorder the terms:
27 + 39y + 4y2 = -6 + 6 + -8y + 8y

Combine like terms: -6 + 6 = 0
27 + 39y + 4y2 = 0 + -8y + 8y
27 + 39y + 4y2 = -8y + 8y

Combine like terms: -8y + 8y = 0
27 + 39y + 4y2 = 0

Factor a trinomial.
(9 + y)(3 + 4y) = 0


Subproblem 1
Set the factor '(9 + y)' equal to zero and attempt to solve:

Simplifying
9 + y = 0

Solving
9 + y = 0

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

Add '-9' to each side of the equation.
9 + -9 + y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + y = 0 + -9
y = 0 + -9

Combine like terms: 0 + -9 = -9
y = -9

Simplifying
y = -9

Subproblem 2
Set the factor '(3 + 4y)' equal to zero and attempt to solve:

Simplifying
3 + 4y = 0

Solving
3 + 4y = 0

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

Add '-3' to each side of the equation.
3 + -3 + 4y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4y = 0 + -3
4y = 0 + -3

Combine like terms: 0 + -3 = -3
4y = -3

Divide each side by '4'.
y = -0.75

Simplifying
y = -0.75
Solution
y = {-9, -0.75}

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