(8y+4)(7y+12)-(13y+2)(8y+4)=0

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Solution for (8y+4)(7y+12)-(13y+2)(8y+4)=0 equation: 


Simplifying
(8y + 4)(7y + 12) + -1(13y + 2)(8y + 4) = 0

Reorder the terms:
(4 + 8y)(7y + 12) + -1(13y + 2)(8y + 4) = 0

Reorder the terms:
(4 + 8y)(12 + 7y) + -1(13y + 2)(8y + 4) = 0

Multiply (4 + 8y) * (12 + 7y)
(4(12 + 7y) + 8y * (12 + 7y)) + -1(13y + 2)(8y + 4) = 0
((12 * 4 + 7y * 4) + 8y * (12 + 7y)) + -1(13y + 2)(8y + 4) = 0
((48 + 28y) + 8y * (12 + 7y)) + -1(13y + 2)(8y + 4) = 0
(48 + 28y + (12 * 8y + 7y * 8y)) + -1(13y + 2)(8y + 4) = 0
(48 + 28y + (96y + 56y2)) + -1(13y + 2)(8y + 4) = 0

Combine like terms: 28y + 96y = 124y
(48 + 124y + 56y2) + -1(13y + 2)(8y + 4) = 0

Reorder the terms:
48 + 124y + 56y2 + -1(2 + 13y)(8y + 4) = 0

Reorder the terms:
48 + 124y + 56y2 + -1(2 + 13y)(4 + 8y) = 0

Multiply (2 + 13y) * (4 + 8y)
48 + 124y + 56y2 + -1(2(4 + 8y) + 13y * (4 + 8y)) = 0
48 + 124y + 56y2 + -1((4 * 2 + 8y * 2) + 13y * (4 + 8y)) = 0
48 + 124y + 56y2 + -1((8 + 16y) + 13y * (4 + 8y)) = 0
48 + 124y + 56y2 + -1(8 + 16y + (4 * 13y + 8y * 13y)) = 0
48 + 124y + 56y2 + -1(8 + 16y + (52y + 104y2)) = 0

Combine like terms: 16y + 52y = 68y
48 + 124y + 56y2 + -1(8 + 68y + 104y2) = 0
48 + 124y + 56y2 + (8 * -1 + 68y * -1 + 104y2 * -1) = 0
48 + 124y + 56y2 + (-8 + -68y + -104y2) = 0

Reorder the terms:
48 + -8 + 124y + -68y + 56y2 + -104y2 = 0

Combine like terms: 48 + -8 = 40
40 + 124y + -68y + 56y2 + -104y2 = 0

Combine like terms: 124y + -68y = 56y
40 + 56y + 56y2 + -104y2 = 0

Combine like terms: 56y2 + -104y2 = -48y2
40 + 56y + -48y2 = 0

Solving
40 + 56y + -48y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '8'.
8(5 + 7y + -6y2) = 0

Factor a trinomial.
8((5 + -3y)(1 + 2y)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(5 + -3y)' equal to zero and attempt to solve:

Simplifying
5 + -3y = 0

Solving
5 + -3y = 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 + -3y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3y = 0 + -5
-3y = 0 + -5

Combine like terms: 0 + -5 = -5
-3y = -5

Divide each side by '-3'.
y = 1.666666667

Simplifying
y = 1.666666667

Subproblem 2
Set the factor '(1 + 2y)' equal to zero and attempt to solve:

Simplifying
1 + 2y = 0

Solving
1 + 2y = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2y = 0 + -1
2y = 0 + -1

Combine like terms: 0 + -1 = -1
2y = -1

Divide each side by '2'.
y = -0.5

Simplifying
y = -0.5
Solution
y = {1.666666667, -0.5}

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