2y(y+3)=5(y+3)

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Solution for 2y(y+3)=5(y+3) equation: 


Simplifying
2y(y + 3) = 5(y + 3)

Reorder the terms:
2y(3 + y) = 5(y + 3)
(3 * 2y + y * 2y) = 5(y + 3)
(6y + 2y2) = 5(y + 3)

Reorder the terms:
6y + 2y2 = 5(3 + y)
6y + 2y2 = (3 * 5 + y * 5)
6y + 2y2 = (15 + 5y)

Solving
6y + 2y2 = 15 + 5y

Solving for variable 'y'.

Reorder the terms:
-15 + 6y + -5y + 2y2 = 15 + 5y + -15 + -5y

Combine like terms: 6y + -5y = 1y
-15 + 1y + 2y2 = 15 + 5y + -15 + -5y

Reorder the terms:
-15 + 1y + 2y2 = 15 + -15 + 5y + -5y

Combine like terms: 15 + -15 = 0
-15 + 1y + 2y2 = 0 + 5y + -5y
-15 + 1y + 2y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
-15 + 1y + 2y2 = 0

Factor a trinomial.
(-3 + -1y)(5 + -2y) = 0


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

Simplifying
-3 + -1y = 0

Solving
-3 + -1y = 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 + -1y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1y = 0 + 3
-1y = 0 + 3

Combine like terms: 0 + 3 = 3
-1y = 3

Divide each side by '-1'.
y = -3

Simplifying
y = -3

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 = {-3, 2.5}

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