3y(y+5)=18

Solution for 3y(y+5)=18 equation:

Simplifying
3y(y + 5) = 18

Reorder the terms:
3y(5 + y) = 18
(5 * 3y + y * 3y) = 18
(15y + 3y2) = 18

Solving
15y + 3y2 = 18

Solving for variable 'y'.

Reorder the terms:
-18 + 15y + 3y2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 15y + 3y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + 5y + y2) = 0

Factor a trinomial.
3((-6 + -1y)(1 + -1y)) = 0

Ignore the factor 3.
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 '(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 = {-6, 1}