4y(17y-9)=180

Solution for 4y(17y-9)=180 equation:

Simplifying
4y(17y + -9) = 180

Reorder the terms:
4y(-9 + 17y) = 180
(-9 * 4y + 17y * 4y) = 180
(-36y + 68y2) = 180

Solving
-36y + 68y2 = 180

Solving for variable 'y'.

Reorder the terms:
-180 + -36y + 68y2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -36y + 68y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-45 + -9y + 17y2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-45 + -9y + 17y2)' equal to zero and attempt to solve:

Simplifying
-45 + -9y + 17y2 = 0

Solving
-45 + -9y + 17y2 = 0

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

Divide each side by '17'.
-2.647058824 + -0.5294117647y + y2 = 0

Move the constant term to the right:

Add '2.647058824' to each side of the equation.
-2.647058824 + -0.5294117647y + 2.647058824 + y2 = 0 + 2.647058824

Reorder the terms:
-2.647058824 + 2.647058824 + -0.5294117647y + y2 = 0 + 2.647058824

Combine like terms: -2.647058824 + 2.647058824 = 0.000000000
0.000000000 + -0.5294117647y + y2 = 0 + 2.647058824
-0.5294117647y + y2 = 0 + 2.647058824

Combine like terms: 0 + 2.647058824 = 2.647058824
-0.5294117647y + y2 = 2.647058824

The y term is -0.5294117647y.  Take half its coefficient (-0.2647058824).
Square it (0.07006920418) and add it to both sides.

Add '0.07006920418' to each side of the equation.
-0.5294117647y + 0.07006920418 + y2 = 2.647058824 + 0.07006920418

Reorder the terms:
0.07006920418 + -0.5294117647y + y2 = 2.647058824 + 0.07006920418

Combine like terms: 2.647058824 + 0.07006920418 = 2.71712802818
0.07006920418 + -0.5294117647y + y2 = 2.71712802818

Factor a perfect square on the left side:
(y + -0.2647058824)(y + -0.2647058824) = 2.71712802818

Calculate the square root of the right side: 1.648371326

Break this problem into two subproblems by setting 
(y + -0.2647058824) equal to 1.648371326 and -1.648371326.

Subproblem 1
y + -0.2647058824 = 1.648371326

Simplifying
y + -0.2647058824 = 1.648371326

Reorder the terms:
-0.2647058824 + y = 1.648371326

Solving
-0.2647058824 + y = 1.648371326

Solving for variable 'y'.

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

Add '0.2647058824' to each side of the equation.
-0.2647058824 + 0.2647058824 + y = 1.648371326 + 0.2647058824

Combine like terms: -0.2647058824 + 0.2647058824 = 0.0000000000
0.0000000000 + y = 1.648371326 + 0.2647058824
y = 1.648371326 + 0.2647058824

Combine like terms: 1.648371326 + 0.2647058824 = 1.9130772084
y = 1.9130772084

Simplifying
y = 1.9130772084

Subproblem 2
y + -0.2647058824 = -1.648371326

Simplifying
y + -0.2647058824 = -1.648371326

Reorder the terms:
-0.2647058824 + y = -1.648371326

Solving
-0.2647058824 + y = -1.648371326

Solving for variable 'y'.

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

Add '0.2647058824' to each side of the equation.
-0.2647058824 + 0.2647058824 + y = -1.648371326 + 0.2647058824

Combine like terms: -0.2647058824 + 0.2647058824 = 0.0000000000
0.0000000000 + y = -1.648371326 + 0.2647058824
y = -1.648371326 + 0.2647058824

Combine like terms: -1.648371326 + 0.2647058824 = -1.3836654436
y = -1.3836654436

Simplifying
y = -1.3836654436

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.9130772084, -1.3836654436}
Solution
y = {1.9130772084, -1.3836654436}