(3y+5)(6y+11)+(2y+15)(3y+5)=0

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Solution for (3y+5)(6y+11)+(2y+15)(3y+5)=0 equation: 


Simplifying
(3y + 5)(6y + 11) + (2y + 15)(3y + 5) = 0

Reorder the terms:
(5 + 3y)(6y + 11) + (2y + 15)(3y + 5) = 0

Reorder the terms:
(5 + 3y)(11 + 6y) + (2y + 15)(3y + 5) = 0

Multiply (5 + 3y) * (11 + 6y)
(5(11 + 6y) + 3y * (11 + 6y)) + (2y + 15)(3y + 5) = 0
((11 * 5 + 6y * 5) + 3y * (11 + 6y)) + (2y + 15)(3y + 5) = 0
((55 + 30y) + 3y * (11 + 6y)) + (2y + 15)(3y + 5) = 0
(55 + 30y + (11 * 3y + 6y * 3y)) + (2y + 15)(3y + 5) = 0
(55 + 30y + (33y + 18y2)) + (2y + 15)(3y + 5) = 0

Combine like terms: 30y + 33y = 63y
(55 + 63y + 18y2) + (2y + 15)(3y + 5) = 0

Reorder the terms:
55 + 63y + 18y2 + (15 + 2y)(3y + 5) = 0

Reorder the terms:
55 + 63y + 18y2 + (15 + 2y)(5 + 3y) = 0

Multiply (15 + 2y) * (5 + 3y)
55 + 63y + 18y2 + (15(5 + 3y) + 2y * (5 + 3y)) = 0
55 + 63y + 18y2 + ((5 * 15 + 3y * 15) + 2y * (5 + 3y)) = 0
55 + 63y + 18y2 + ((75 + 45y) + 2y * (5 + 3y)) = 0
55 + 63y + 18y2 + (75 + 45y + (5 * 2y + 3y * 2y)) = 0
55 + 63y + 18y2 + (75 + 45y + (10y + 6y2)) = 0

Combine like terms: 45y + 10y = 55y
55 + 63y + 18y2 + (75 + 55y + 6y2) = 0

Reorder the terms:
55 + 75 + 63y + 55y + 18y2 + 6y2 = 0

Combine like terms: 55 + 75 = 130
130 + 63y + 55y + 18y2 + 6y2 = 0

Combine like terms: 63y + 55y = 118y
130 + 118y + 18y2 + 6y2 = 0

Combine like terms: 18y2 + 6y2 = 24y2
130 + 118y + 24y2 = 0

Solving
130 + 118y + 24y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(65 + 59y + 12y2) = 0

Factor a trinomial.
2((13 + 4y)(5 + 3y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(13 + 4y)' equal to zero and attempt to solve:

Simplifying
13 + 4y = 0

Solving
13 + 4y = 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 + 4y = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 4y = 0 + -13
4y = 0 + -13

Combine like terms: 0 + -13 = -13
4y = -13

Divide each side by '4'.
y = -3.25

Simplifying
y = -3.25

Subproblem 2
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
Solution
y = {-3.25, -1.666666667}

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