2y(y+5)=48

Solution for 2y(y+5)=48 equation:

Simplifying
2y(y + 5) = 48

Reorder the terms:
2y(5 + y) = 48
(5 * 2y + y * 2y) = 48
(10y + 2y2) = 48

Solving
10y + 2y2 = 48

Solving for variable 'y'.

Reorder the terms:
-48 + 10y + 2y2 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + 10y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + 5y + y2) = 0

Factor a trinomial.
2((-8 + -1y)(3 + -1y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -1y)' equal to zero and attempt to solve:

Simplifying
-8 + -1y = 0

Solving
-8 + -1y = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1y = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1y = 0 + 8
-1y = 0 + 8

Combine like terms: 0 + 8 = 8
-1y = 8

Divide each side by '-1'.
y = -8

Simplifying
y = -8
Subproblem 2
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
Solution
y = {-8, 3}