4y^2+24y-24=0

Solution for 4y^2+24y-24=0 equation:

Simplifying
4y2 + 24y + -24 = 0

Reorder the terms:
-24 + 24y + 4y2 = 0

Solving
-24 + 24y + 4y2 = 0

Solving for variable 'y'.

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

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

Simplifying
-6 + 6y + y2 = 0

Solving
-6 + 6y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 6y + 6 + y2 = 0 + 6

Reorder the terms:
-6 + 6 + 6y + y2 = 0 + 6

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

Combine like terms: 0 + 6 = 6
6y + y2 = 6

The y term is 6y.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6y + 9 + y2 = 6 + 9

Reorder the terms:
9 + 6y + y2 = 6 + 9

Combine like terms: 6 + 9 = 15
9 + 6y + y2 = 15

Factor a perfect square on the left side:
(y + 3)(y + 3) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(y + 3) equal to 3.872983346 and -3.872983346.

Subproblem 1
y + 3 = 3.872983346

Simplifying
y + 3 = 3.872983346

Reorder the terms:
3 + y = 3.872983346

Solving
3 + y = 3.872983346

Solving for variable 'y'.

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

Add '-3' to each side of the equation.
3 + -3 + y = 3.872983346 + -3

Combine like terms: 3 + -3 = 0
0 + y = 3.872983346 + -3
y = 3.872983346 + -3

Combine like terms: 3.872983346 + -3 = 0.872983346
y = 0.872983346

Simplifying
y = 0.872983346

Subproblem 2
y + 3 = -3.872983346

Simplifying
y + 3 = -3.872983346

Reorder the terms:
3 + y = -3.872983346

Solving
3 + y = -3.872983346

Solving for variable 'y'.

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

Add '-3' to each side of the equation.
3 + -3 + y = -3.872983346 + -3

Combine like terms: 3 + -3 = 0
0 + y = -3.872983346 + -3
y = -3.872983346 + -3

Combine like terms: -3.872983346 + -3 = -6.872983346
y = -6.872983346

Simplifying
y = -6.872983346

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.872983346, -6.872983346}
Solution
y = {0.872983346, -6.872983346}