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

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


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

Reorder the terms:
4y(5 + y) = 5(y + 5)
(5 * 4y + y * 4y) = 5(y + 5)
(20y + 4y2) = 5(y + 5)

Reorder the terms:
20y + 4y2 = 5(5 + y)
20y + 4y2 = (5 * 5 + y * 5)
20y + 4y2 = (25 + 5y)

Solving
20y + 4y2 = 25 + 5y

Solving for variable 'y'.

Reorder the terms:
-25 + 20y + -5y + 4y2 = 25 + 5y + -25 + -5y

Combine like terms: 20y + -5y = 15y
-25 + 15y + 4y2 = 25 + 5y + -25 + -5y

Reorder the terms:
-25 + 15y + 4y2 = 25 + -25 + 5y + -5y

Combine like terms: 25 + -25 = 0
-25 + 15y + 4y2 = 0 + 5y + -5y
-25 + 15y + 4y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
-25 + 15y + 4y2 = 0

Factor a trinomial.
(-5 + -1y)(5 + -4y) = 0


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

Simplifying
-5 + -1y = 0

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

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

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

Divide each side by '-1'.
y = -5

Simplifying
y = -5

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 = {-5, 1.25}

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