2y(y+5)=72

Solution for 2y(y+5)=72 equation:

Simplifying
2y(y + 5) = 72

Reorder the terms:
2y(5 + y) = 72
(5 * 2y + y * 2y) = 72
(10y + 2y2) = 72

Solving
10y + 2y2 = 72

Solving for variable 'y'.

Reorder the terms:
-72 + 10y + 2y2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + 10y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + 5y + y2) = 0

Factor a trinomial.
2((-9 + -1y)(4 + -1y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + -1y)' equal to zero and attempt to solve:

Simplifying
-9 + -1y = 0

Solving
-9 + -1y = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1y = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1y = 0 + 9
-1y = 0 + 9

Combine like terms: 0 + 9 = 9
-1y = 9

Divide each side by '-1'.
y = -9

Simplifying
y = -9
Subproblem 2
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {-9, 4}