2y(y+2)=5(y+2)

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Solution for 2y(y+2)=5(y+2) equation: 


Simplifying
2y(y + 2) = 5(y + 2)

Reorder the terms:
2y(2 + y) = 5(y + 2)
(2 * 2y + y * 2y) = 5(y + 2)
(4y + 2y2) = 5(y + 2)

Reorder the terms:
4y + 2y2 = 5(2 + y)
4y + 2y2 = (2 * 5 + y * 5)
4y + 2y2 = (10 + 5y)

Solving
4y + 2y2 = 10 + 5y

Solving for variable 'y'.

Reorder the terms:
-10 + 4y + -5y + 2y2 = 10 + 5y + -10 + -5y

Combine like terms: 4y + -5y = -1y
-10 + -1y + 2y2 = 10 + 5y + -10 + -5y

Reorder the terms:
-10 + -1y + 2y2 = 10 + -10 + 5y + -5y

Combine like terms: 10 + -10 = 0
-10 + -1y + 2y2 = 0 + 5y + -5y
-10 + -1y + 2y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
-10 + -1y + 2y2 = 0

Factor a trinomial.
(-2 + -1y)(5 + -2y) = 0


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

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1y = 0 + 2
-1y = 0 + 2

Combine like terms: 0 + 2 = 2
-1y = 2

Divide each side by '-1'.
y = -2

Simplifying
y = -2

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

Simplifying
5 + -2y = 0

Solving
5 + -2y = 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 + -2y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2y = 0 + -5
-2y = 0 + -5

Combine like terms: 0 + -5 = -5
-2y = -5

Divide each side by '-2'.
y = 2.5

Simplifying
y = 2.5
Solution
y = {-2, 2.5}

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