6y+24=4y(3y+3)

Solution for 6y+24=4y(3y+3) equation:

Simplifying
6y + 24 = 4y(3y + 3)

Reorder the terms:
24 + 6y = 4y(3y + 3)

Reorder the terms:
24 + 6y = 4y(3 + 3y)
24 + 6y = (3 * 4y + 3y * 4y)
24 + 6y = (12y + 12y2)

Solving
24 + 6y = 12y + 12y2

Solving for variable 'y'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), '6'.
6(4 + -1y + -2y2) = 0

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

Simplifying
4 + -1y + -2y2 = 0

Solving
4 + -1y + -2y2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-2 + 0.5y + y2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 0.5y + 2 + y2 = 0 + 2

Reorder the terms:
-2 + 2 + 0.5y + y2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 0.5y + y2 = 0 + 2
0.5y + y2 = 0 + 2

Combine like terms: 0 + 2 = 2
0.5y + y2 = 2

The y term is 0.5y.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5y + 0.0625 + y2 = 2 + 0.0625

Reorder the terms:
0.0625 + 0.5y + y2 = 2 + 0.0625

Combine like terms: 2 + 0.0625 = 2.0625
0.0625 + 0.5y + y2 = 2.0625

Factor a perfect square on the left side:
(y + 0.25)(y + 0.25) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(y + 0.25) equal to 1.436140662 and -1.436140662.

Subproblem 1
y + 0.25 = 1.436140662

Simplifying
y + 0.25 = 1.436140662

Reorder the terms:
0.25 + y = 1.436140662

Solving
0.25 + y = 1.436140662

Solving for variable 'y'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + y = 1.436140662 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + y = 1.436140662 + -0.25
y = 1.436140662 + -0.25

Combine like terms: 1.436140662 + -0.25 = 1.186140662
y = 1.186140662

Simplifying
y = 1.186140662

Subproblem 2
y + 0.25 = -1.436140662

Simplifying
y + 0.25 = -1.436140662

Reorder the terms:
0.25 + y = -1.436140662

Solving
0.25 + y = -1.436140662

Solving for variable 'y'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + y = -1.436140662 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + y = -1.436140662 + -0.25
y = -1.436140662 + -0.25

Combine like terms: -1.436140662 + -0.25 = -1.686140662
y = -1.686140662

Simplifying
y = -1.686140662

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.186140662, -1.686140662}
Solution
y = {1.186140662, -1.686140662}