2y(y+6)=5(y+6)

Solution for 2y(y+6)=5(y+6) equation:

Simplifying
2y(y + 6) = 5(y + 6)

Reorder the terms:
2y(6 + y) = 5(y + 6)
(6 * 2y + y * 2y) = 5(y + 6)
(12y + 2y2) = 5(y + 6)

Reorder the terms:
12y + 2y2 = 5(6 + y)
12y + 2y2 = (6 * 5 + y * 5)
12y + 2y2 = (30 + 5y)

Solving
12y + 2y2 = 30 + 5y

Solving for variable 'y'.

Reorder the terms:
-30 + 12y + -5y + 2y2 = 30 + 5y + -30 + -5y

Combine like terms: 12y + -5y = 7y
-30 + 7y + 2y2 = 30 + 5y + -30 + -5y

Reorder the terms:
-30 + 7y + 2y2 = 30 + -30 + 5y + -5y

Combine like terms: 30 + -30 = 0
-30 + 7y + 2y2 = 0 + 5y + -5y
-30 + 7y + 2y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
-30 + 7y + 2y2 = 0

Factor a trinomial.
(-6 + -1y)(5 + -2y) = 0

Subproblem 1
Set the factor '(-6 + -1y)' equal to zero and attempt to solve:

Simplifying
-6 + -1y = 0

Solving
-6 + -1y = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1y = 0 + 6
-1y = 0 + 6

Combine like terms: 0 + 6 = 6
-1y = 6

Divide each side by '-1'.
y = -6

Simplifying
y = -6
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 = {-6, 2.5}