4y(y+8)=5(y+8)

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Solution for 4y(y+8)=5(y+8) equation: 


Simplifying
4y(y + 8) = 5(y + 8)

Reorder the terms:
4y(8 + y) = 5(y + 8)
(8 * 4y + y * 4y) = 5(y + 8)
(32y + 4y2) = 5(y + 8)

Reorder the terms:
32y + 4y2 = 5(8 + y)
32y + 4y2 = (8 * 5 + y * 5)
32y + 4y2 = (40 + 5y)

Solving
32y + 4y2 = 40 + 5y

Solving for variable 'y'.

Reorder the terms:
-40 + 32y + -5y + 4y2 = 40 + 5y + -40 + -5y

Combine like terms: 32y + -5y = 27y
-40 + 27y + 4y2 = 40 + 5y + -40 + -5y

Reorder the terms:
-40 + 27y + 4y2 = 40 + -40 + 5y + -5y

Combine like terms: 40 + -40 = 0
-40 + 27y + 4y2 = 0 + 5y + -5y
-40 + 27y + 4y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
-40 + 27y + 4y2 = 0

Factor a trinomial.
(-8 + -1y)(5 + -4y) = 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 '(5 + -4y)' equal to zero and attempt to solve:

Simplifying
5 + -4y = 0

Solving
5 + -4y = 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 + -4y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4y = 0 + -5
-4y = 0 + -5

Combine like terms: 0 + -5 = -5
-4y = -5

Divide each side by '-4'.
y = 1.25

Simplifying
y = 1.25
Solution
y = {-8, 1.25}

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