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

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


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

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

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

Multiply (3 + 4y) * (3 + y)
(3(3 + y) + 4y * (3 + y)) = -4(4y + 3)
((3 * 3 + y * 3) + 4y * (3 + y)) = -4(4y + 3)
((9 + 3y) + 4y * (3 + y)) = -4(4y + 3)
(9 + 3y + (3 * 4y + y * 4y)) = -4(4y + 3)
(9 + 3y + (12y + 4y2)) = -4(4y + 3)

Combine like terms: 3y + 12y = 15y
(9 + 15y + 4y2) = -4(4y + 3)

Reorder the terms:
9 + 15y + 4y2 = -4(3 + 4y)
9 + 15y + 4y2 = (3 * -4 + 4y * -4)
9 + 15y + 4y2 = (-12 + -16y)

Solving
9 + 15y + 4y2 = -12 + -16y

Solving for variable 'y'.

Reorder the terms:
9 + 12 + 15y + 16y + 4y2 = -12 + -16y + 12 + 16y

Combine like terms: 9 + 12 = 21
21 + 15y + 16y + 4y2 = -12 + -16y + 12 + 16y

Combine like terms: 15y + 16y = 31y
21 + 31y + 4y2 = -12 + -16y + 12 + 16y

Reorder the terms:
21 + 31y + 4y2 = -12 + 12 + -16y + 16y

Combine like terms: -12 + 12 = 0
21 + 31y + 4y2 = 0 + -16y + 16y
21 + 31y + 4y2 = -16y + 16y

Combine like terms: -16y + 16y = 0
21 + 31y + 4y2 = 0

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


Subproblem 1
Set the factor '(7 + y)' equal to zero and attempt to solve:

Simplifying
7 + y = 0

Solving
7 + y = 0

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

Add '-7' to each side of the equation.
7 + -7 + y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + y = 0 + -7
y = 0 + -7

Combine like terms: 0 + -7 = -7
y = -7

Simplifying
y = -7

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 = {-7, -0.75}

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