(5y+13)(3y+8)=0

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Solution for (5y+13)(3y+8)=0 equation: 


Simplifying
(5y + 13)(3y + 8) = 0

Reorder the terms:
(13 + 5y)(3y + 8) = 0

Reorder the terms:
(13 + 5y)(8 + 3y) = 0

Multiply (13 + 5y) * (8 + 3y)
(13(8 + 3y) + 5y * (8 + 3y)) = 0
((8 * 13 + 3y * 13) + 5y * (8 + 3y)) = 0
((104 + 39y) + 5y * (8 + 3y)) = 0
(104 + 39y + (8 * 5y + 3y * 5y)) = 0
(104 + 39y + (40y + 15y2)) = 0

Combine like terms: 39y + 40y = 79y
(104 + 79y + 15y2) = 0

Solving
104 + 79y + 15y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(8 + 3y)(13 + 5y) = 0


Subproblem 1
Set the factor '(8 + 3y)' equal to zero and attempt to solve:

Simplifying
8 + 3y = 0

Solving
8 + 3y = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3y = 0 + -8
3y = 0 + -8

Combine like terms: 0 + -8 = -8
3y = -8

Divide each side by '3'.
y = -2.666666667

Simplifying
y = -2.666666667

Subproblem 2
Set the factor '(13 + 5y)' equal to zero and attempt to solve:

Simplifying
13 + 5y = 0

Solving
13 + 5y = 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 + 5y = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 5y = 0 + -13
5y = 0 + -13

Combine like terms: 0 + -13 = -13
5y = -13

Divide each side by '5'.
y = -2.6

Simplifying
y = -2.6
Solution
y = {-2.666666667, -2.6}

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