2y(3y-6)=24

Solution for 2y(3y-6)=24 equation:

Simplifying
2y(3y + -6) = 24

Reorder the terms:
2y(-6 + 3y) = 24
(-6 * 2y + 3y * 2y) = 24
(-12y + 6y2) = 24

Solving
-12y + 6y2 = 24

Solving for variable 'y'.

Reorder the terms:
-24 + -12y + 6y2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + -12y + 6y2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-4 + -2y + y2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-4 + -2y + y2)' equal to zero and attempt to solve:

Simplifying
-4 + -2y + y2 = 0

Solving
-4 + -2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -2y + 4 + y2 = 0 + 4

Reorder the terms:
-4 + 4 + -2y + y2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -2y + y2 = 0 + 4
-2y + y2 = 0 + 4

Combine like terms: 0 + 4 = 4
-2y + y2 = 4

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = 4 + 1

Reorder the terms:
1 + -2y + y2 = 4 + 1

Combine like terms: 4 + 1 = 5
1 + -2y + y2 = 5

Factor a perfect square on the left side:
(y + -1)(y + -1) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(y + -1) equal to 2.236067978 and -2.236067978.

Subproblem 1
y + -1 = 2.236067978

Simplifying
y + -1 = 2.236067978

Reorder the terms:
-1 + y = 2.236067978

Solving
-1 + y = 2.236067978

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = 2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + y = 2.236067978 + 1
y = 2.236067978 + 1

Combine like terms: 2.236067978 + 1 = 3.236067978
y = 3.236067978

Simplifying
y = 3.236067978

Subproblem 2
y + -1 = -2.236067978

Simplifying
y + -1 = -2.236067978

Reorder the terms:
-1 + y = -2.236067978

Solving
-1 + y = -2.236067978

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = -2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + y = -2.236067978 + 1
y = -2.236067978 + 1

Combine like terms: -2.236067978 + 1 = -1.236067978
y = -1.236067978

Simplifying
y = -1.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.236067978, -1.236067978}
Solution
y = {3.236067978, -1.236067978}