24=4y^2-8y

Solution for 24=4y^2-8y equation:

Simplifying
24 = 4y2 + -8y

Reorder the terms:
24 = -8y + 4y2

Solving
24 = -8y + 4y2

Solving for variable 'y'.

Reorder the terms:
24 + 8y + -4y2 = -8y + 8y + 4y2 + -4y2

Combine like terms: -8y + 8y = 0
24 + 8y + -4y2 = 0 + 4y2 + -4y2
24 + 8y + -4y2 = 4y2 + -4y2

Combine like terms: 4y2 + -4y2 = 0
24 + 8y + -4y2 = 0

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

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

Simplifying
6 + 2y + -1y2 = 0

Solving
6 + 2y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + -2y + y2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -2y + 6 + y2 = 0 + 6

Reorder the terms:
-6 + 6 + -2y + y2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -2y + y2 = 0 + 6
-2y + y2 = 0 + 6

Combine like terms: 0 + 6 = 6
-2y + y2 = 6

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 = 6 + 1

Reorder the terms:
1 + -2y + y2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + -2y + y2 = 7

Factor a perfect square on the left side:
(y + -1)(y + -1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(y + -1) equal to 2.645751311 and -2.645751311.

Subproblem 1
y + -1 = 2.645751311

Simplifying
y + -1 = 2.645751311

Reorder the terms:
-1 + y = 2.645751311

Solving
-1 + y = 2.645751311

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 = 2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + y = 2.645751311 + 1
y = 2.645751311 + 1

Combine like terms: 2.645751311 + 1 = 3.645751311
y = 3.645751311

Simplifying
y = 3.645751311

Subproblem 2
y + -1 = -2.645751311

Simplifying
y + -1 = -2.645751311

Reorder the terms:
-1 + y = -2.645751311

Solving
-1 + y = -2.645751311

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 = -2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + y = -2.645751311 + 1
y = -2.645751311 + 1

Combine like terms: -2.645751311 + 1 = -1.645751311
y = -1.645751311

Simplifying
y = -1.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.645751311, -1.645751311}
Solution
y = {3.645751311, -1.645751311}