3y(2y+1)=18

Solution for 3y(2y+1)=18 equation:

Simplifying
3y(2y + 1) = 18

Reorder the terms:
3y(1 + 2y) = 18
(1 * 3y + 2y * 3y) = 18
(3y + 6y2) = 18

Solving
3y + 6y2 = 18

Solving for variable 'y'.

Reorder the terms:
-18 + 3y + 6y2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 3y + 6y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + y + 2y2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + -1y)' equal to zero and attempt to solve:

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1y = 0 + 2
-1y = 0 + 2

Combine like terms: 0 + 2 = 2
-1y = 2

Divide each side by '-1'.
y = -2

Simplifying
y = -2
Subproblem 2
Set the factor '(3 + -2y)' equal to zero and attempt to solve:

Simplifying
3 + -2y = 0

Solving
3 + -2y = 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 + -2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2y = 0 + -3
-2y = 0 + -3

Combine like terms: 0 + -3 = -3
-2y = -3

Divide each side by '-2'.
y = 1.5

Simplifying
y = 1.5
Solution
y = {-2, 1.5}