9y-4y(y-2)=3

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Solution for 9y-4y(y-2)=3 equation: 


Simplifying
9y + -4y(y + -2) = 3

Reorder the terms:
9y + -4y(-2 + y) = 3
9y + (-2 * -4y + y * -4y) = 3
9y + (8y + -4y2) = 3

Combine like terms: 9y + 8y = 17y
17y + -4y2 = 3

Solving
17y + -4y2 = 3

Solving for variable 'y'.

Reorder the terms:
-3 + 17y + -4y2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 17y + -4y2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
0.75 + -4.25y + y2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -4.25y + -0.75 + y2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -4.25y + y2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -4.25y + y2 = 0 + -0.75
-4.25y + y2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-4.25y + y2 = -0.75

The y term is -4.25y.  Take half its coefficient (-2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
-4.25y + 4.515625 + y2 = -0.75 + 4.515625

Reorder the terms:
4.515625 + -4.25y + y2 = -0.75 + 4.515625

Combine like terms: -0.75 + 4.515625 = 3.765625
4.515625 + -4.25y + y2 = 3.765625

Factor a perfect square on the left side:
(y + -2.125)(y + -2.125) = 3.765625

Calculate the square root of the right side: 1.940521837

Break this problem into two subproblems by setting 
(y + -2.125) equal to 1.940521837 and -1.940521837.


Subproblem 1
y + -2.125 = 1.940521837

Simplifying
y + -2.125 = 1.940521837

Reorder the terms:
-2.125 + y = 1.940521837

Solving
-2.125 + y = 1.940521837

Solving for variable 'y'.

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

Add '2.125' to each side of the equation.
-2.125 + 2.125 + y = 1.940521837 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + y = 1.940521837 + 2.125
y = 1.940521837 + 2.125

Combine like terms: 1.940521837 + 2.125 = 4.065521837
y = 4.065521837

Simplifying
y = 4.065521837


Subproblem 2
y + -2.125 = -1.940521837

Simplifying
y + -2.125 = -1.940521837

Reorder the terms:
-2.125 + y = -1.940521837

Solving
-2.125 + y = -1.940521837

Solving for variable 'y'.

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

Add '2.125' to each side of the equation.
-2.125 + 2.125 + y = -1.940521837 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + y = -1.940521837 + 2.125
y = -1.940521837 + 2.125

Combine like terms: -1.940521837 + 2.125 = 0.184478163
y = 0.184478163

Simplifying
y = 0.184478163


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.065521837, 0.184478163}

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