20(2y^2-y-9)=0

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Solution for 20(2y^2-y-9)=0 equation: 


Simplifying
20(2y2 + -1y + -9) = 0

Reorder the terms:
20(-9 + -1y + 2y2) = 0
(-9 * 20 + -1y * 20 + 2y2 * 20) = 0
(-180 + -20y + 40y2) = 0

Solving
-180 + -20y + 40y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '20'.
20(-9 + -1y + 2y2) = 0

Ignore the factor 20.

Subproblem 1
Set the factor '(-9 + -1y + 2y2)' equal to zero and attempt to solve:

Simplifying
-9 + -1y + 2y2 = 0

Solving
-9 + -1y + 2y2 = 0

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

Divide each side by '2'.
-4.5 + -0.5y + y2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -0.5y + 4.5 + y2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -0.5y + y2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -0.5y + y2 = 0 + 4.5
-0.5y + y2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-0.5y + y2 = 4.5

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 = 4.5 + 0.0625

Reorder the terms:
0.0625 + -0.5y + y2 = 4.5 + 0.0625

Combine like terms: 4.5 + 0.0625 = 4.5625
0.0625 + -0.5y + y2 = 4.5625

Factor a perfect square on the left side:
(y + -0.25)(y + -0.25) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(y + -0.25) equal to 2.136000936 and -2.136000936.


Subproblem 1
y + -0.25 = 2.136000936

Simplifying
y + -0.25 = 2.136000936

Reorder the terms:
-0.25 + y = 2.136000936

Solving
-0.25 + y = 2.136000936

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 = 2.136000936 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + y = 2.136000936 + 0.25
y = 2.136000936 + 0.25

Combine like terms: 2.136000936 + 0.25 = 2.386000936
y = 2.386000936

Simplifying
y = 2.386000936


Subproblem 2
y + -0.25 = -2.136000936

Simplifying
y + -0.25 = -2.136000936

Reorder the terms:
-0.25 + y = -2.136000936

Solving
-0.25 + y = -2.136000936

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 = -2.136000936 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + y = -2.136000936 + 0.25
y = -2.136000936 + 0.25

Combine like terms: -2.136000936 + 0.25 = -1.886000936
y = -1.886000936

Simplifying
y = -1.886000936


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.386000936, -1.886000936}
Solution
y = {2.386000936, -1.886000936}

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