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

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


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

Reorder the terms:
5y(8 + y) = 3(y + 8)
(8 * 5y + y * 5y) = 3(y + 8)
(40y + 5y2) = 3(y + 8)

Reorder the terms:
40y + 5y2 = 3(8 + y)
40y + 5y2 = (8 * 3 + y * 3)
40y + 5y2 = (24 + 3y)

Solving
40y + 5y2 = 24 + 3y

Solving for variable 'y'.

Reorder the terms:
-24 + 40y + -3y + 5y2 = 24 + 3y + -24 + -3y

Combine like terms: 40y + -3y = 37y
-24 + 37y + 5y2 = 24 + 3y + -24 + -3y

Reorder the terms:
-24 + 37y + 5y2 = 24 + -24 + 3y + -3y

Combine like terms: 24 + -24 = 0
-24 + 37y + 5y2 = 0 + 3y + -3y
-24 + 37y + 5y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
-24 + 37y + 5y2 = 0

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


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

Simplifying
-8 + -1y = 0

Solving
-8 + -1y = 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 + -1y = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1y = 0 + 8
-1y = 0 + 8

Combine like terms: 0 + 8 = 8
-1y = 8

Divide each side by '-1'.
y = -8

Simplifying
y = -8

Subproblem 2
Set the factor '(3 + -5y)' equal to zero and attempt to solve:

Simplifying
3 + -5y = 0

Solving
3 + -5y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5y = 0 + -3

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

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

Divide each side by '-5'.
y = 0.6

Simplifying
y = 0.6
Solution
y = {-8, 0.6}

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