-3y^2-3y+24=0

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Solution for -3y^2-3y+24=0 equation: 


Simplifying
-3y2 + -3y + 24 = 0

Reorder the terms:
24 + -3y + -3y2 = 0

Solving
24 + -3y + -3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + -1y + -1y2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(8 + -1y + -1y2)' equal to zero and attempt to solve:

Simplifying
8 + -1y + -1y2 = 0

Solving
8 + -1y + -1y2 = 0

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

Divide each side by '-1'.
-8 + y + y2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + y + 8 + y2 = 0 + 8

Reorder the terms:
-8 + 8 + y + y2 = 0 + 8

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

Combine like terms: 0 + 8 = 8
y + y2 = 8

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

Add '0.25' to each side of the equation.
 + 0.25 + y2 = 8 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + y2 = 8 + 0.25

Combine like terms: 8 + 0.25 = 8.25
1.25 + y2 = 8.25

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(y + 0.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
y + 0.5 = 2.872281323

Simplifying
y + 0.5 = 2.872281323

Reorder the terms:
0.5 + y = 2.872281323

Solving
0.5 + y = 2.872281323

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = 2.872281323 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 2.872281323 + -0.5
y = 2.872281323 + -0.5

Combine like terms: 2.872281323 + -0.5 = 2.372281323
y = 2.372281323

Simplifying
y = 2.372281323


Subproblem 2
y + 0.5 = -2.872281323

Simplifying
y + 0.5 = -2.872281323

Reorder the terms:
0.5 + y = -2.872281323

Solving
0.5 + y = -2.872281323

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = -2.872281323 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -2.872281323 + -0.5
y = -2.872281323 + -0.5

Combine like terms: -2.872281323 + -0.5 = -3.372281323
y = -3.372281323

Simplifying
y = -3.372281323


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.372281323, -3.372281323}
Solution
y = {2.372281323, -3.372281323}

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