3y(y+4)=15

Solution for 3y(y+4)=15 equation:

Simplifying
3y(y + 4) = 15

Reorder the terms:
3y(4 + y) = 15
(4 * 3y + y * 3y) = 15
(12y + 3y2) = 15

Solving
12y + 3y2 = 15

Solving for variable 'y'.

Reorder the terms:
-15 + 12y + 3y2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 12y + 3y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + 4y + y2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -1y)' equal to zero and attempt to solve:

Simplifying
-5 + -1y = 0

Solving
-5 + -1y = 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 + -1y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1y = 0 + 5
-1y = 0 + 5

Combine like terms: 0 + 5 = 5
-1y = 5

Divide each side by '-1'.
y = -5

Simplifying
y = -5
Subproblem 2
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

Simplifying
y = 1
Solution
y = {-5, 1}