(15y+3)(5y+10)+(13y+7)(15y+3)=0

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Solution for (15y+3)(5y+10)+(13y+7)(15y+3)=0 equation: 


Simplifying
(15y + 3)(5y + 10) + (13y + 7)(15y + 3) = 0

Reorder the terms:
(3 + 15y)(5y + 10) + (13y + 7)(15y + 3) = 0

Reorder the terms:
(3 + 15y)(10 + 5y) + (13y + 7)(15y + 3) = 0

Multiply (3 + 15y) * (10 + 5y)
(3(10 + 5y) + 15y * (10 + 5y)) + (13y + 7)(15y + 3) = 0
((10 * 3 + 5y * 3) + 15y * (10 + 5y)) + (13y + 7)(15y + 3) = 0
((30 + 15y) + 15y * (10 + 5y)) + (13y + 7)(15y + 3) = 0
(30 + 15y + (10 * 15y + 5y * 15y)) + (13y + 7)(15y + 3) = 0
(30 + 15y + (150y + 75y2)) + (13y + 7)(15y + 3) = 0

Combine like terms: 15y + 150y = 165y
(30 + 165y + 75y2) + (13y + 7)(15y + 3) = 0

Reorder the terms:
30 + 165y + 75y2 + (7 + 13y)(15y + 3) = 0

Reorder the terms:
30 + 165y + 75y2 + (7 + 13y)(3 + 15y) = 0

Multiply (7 + 13y) * (3 + 15y)
30 + 165y + 75y2 + (7(3 + 15y) + 13y * (3 + 15y)) = 0
30 + 165y + 75y2 + ((3 * 7 + 15y * 7) + 13y * (3 + 15y)) = 0
30 + 165y + 75y2 + ((21 + 105y) + 13y * (3 + 15y)) = 0
30 + 165y + 75y2 + (21 + 105y + (3 * 13y + 15y * 13y)) = 0
30 + 165y + 75y2 + (21 + 105y + (39y + 195y2)) = 0

Combine like terms: 105y + 39y = 144y
30 + 165y + 75y2 + (21 + 144y + 195y2) = 0

Reorder the terms:
30 + 21 + 165y + 144y + 75y2 + 195y2 = 0

Combine like terms: 30 + 21 = 51
51 + 165y + 144y + 75y2 + 195y2 = 0

Combine like terms: 165y + 144y = 309y
51 + 309y + 75y2 + 195y2 = 0

Combine like terms: 75y2 + 195y2 = 270y2
51 + 309y + 270y2 = 0

Solving
51 + 309y + 270y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(17 + 103y + 90y2) = 0

Factor a trinomial.
3((17 + 18y)(1 + 5y)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(17 + 18y)' equal to zero and attempt to solve:

Simplifying
17 + 18y = 0

Solving
17 + 18y = 0

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

Add '-17' to each side of the equation.
17 + -17 + 18y = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 18y = 0 + -17
18y = 0 + -17

Combine like terms: 0 + -17 = -17
18y = -17

Divide each side by '18'.
y = -0.9444444444

Simplifying
y = -0.9444444444

Subproblem 2
Set the factor '(1 + 5y)' equal to zero and attempt to solve:

Simplifying
1 + 5y = 0

Solving
1 + 5y = 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 + 5y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5y = 0 + -1
5y = 0 + -1

Combine like terms: 0 + -1 = -1
5y = -1

Divide each side by '5'.
y = -0.2

Simplifying
y = -0.2
Solution
y = {-0.9444444444, -0.2}

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