(3y+13)(2y+7)+(6y+11)(3y+13)=0

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Solution for (3y+13)(2y+7)+(6y+11)(3y+13)=0 equation: 


Simplifying
(3y + 13)(2y + 7) + (6y + 11)(3y + 13) = 0

Reorder the terms:
(13 + 3y)(2y + 7) + (6y + 11)(3y + 13) = 0

Reorder the terms:
(13 + 3y)(7 + 2y) + (6y + 11)(3y + 13) = 0

Multiply (13 + 3y) * (7 + 2y)
(13(7 + 2y) + 3y * (7 + 2y)) + (6y + 11)(3y + 13) = 0
((7 * 13 + 2y * 13) + 3y * (7 + 2y)) + (6y + 11)(3y + 13) = 0
((91 + 26y) + 3y * (7 + 2y)) + (6y + 11)(3y + 13) = 0
(91 + 26y + (7 * 3y + 2y * 3y)) + (6y + 11)(3y + 13) = 0
(91 + 26y + (21y + 6y2)) + (6y + 11)(3y + 13) = 0

Combine like terms: 26y + 21y = 47y
(91 + 47y + 6y2) + (6y + 11)(3y + 13) = 0

Reorder the terms:
91 + 47y + 6y2 + (11 + 6y)(3y + 13) = 0

Reorder the terms:
91 + 47y + 6y2 + (11 + 6y)(13 + 3y) = 0

Multiply (11 + 6y) * (13 + 3y)
91 + 47y + 6y2 + (11(13 + 3y) + 6y * (13 + 3y)) = 0
91 + 47y + 6y2 + ((13 * 11 + 3y * 11) + 6y * (13 + 3y)) = 0
91 + 47y + 6y2 + ((143 + 33y) + 6y * (13 + 3y)) = 0
91 + 47y + 6y2 + (143 + 33y + (13 * 6y + 3y * 6y)) = 0
91 + 47y + 6y2 + (143 + 33y + (78y + 18y2)) = 0

Combine like terms: 33y + 78y = 111y
91 + 47y + 6y2 + (143 + 111y + 18y2) = 0

Reorder the terms:
91 + 143 + 47y + 111y + 6y2 + 18y2 = 0

Combine like terms: 91 + 143 = 234
234 + 47y + 111y + 6y2 + 18y2 = 0

Combine like terms: 47y + 111y = 158y
234 + 158y + 6y2 + 18y2 = 0

Combine like terms: 6y2 + 18y2 = 24y2
234 + 158y + 24y2 = 0

Solving
234 + 158y + 24y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(117 + 79y + 12y2) = 0

Factor a trinomial.
2((13 + 3y)(9 + 4y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(13 + 3y)' equal to zero and attempt to solve:

Simplifying
13 + 3y = 0

Solving
13 + 3y = 0

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

Add '-13' to each side of the equation.
13 + -13 + 3y = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 3y = 0 + -13
3y = 0 + -13

Combine like terms: 0 + -13 = -13
3y = -13

Divide each side by '3'.
y = -4.333333333

Simplifying
y = -4.333333333

Subproblem 2
Set the factor '(9 + 4y)' equal to zero and attempt to solve:

Simplifying
9 + 4y = 0

Solving
9 + 4y = 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 + 4y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 4y = 0 + -9
4y = 0 + -9

Combine like terms: 0 + -9 = -9
4y = -9

Divide each side by '4'.
y = -2.25

Simplifying
y = -2.25
Solution
y = {-4.333333333, -2.25}

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