5(2-3y)9y=4(3-2y)

Solution for 5(2-3y)9y=4(3-2y) equation:

Simplifying
5(2 + -3y) * 9y = 4(3 + -2y)

Reorder the terms for easier multiplication:
5 * 9y(2 + -3y) = 4(3 + -2y)

Multiply 5 * 9
45y(2 + -3y) = 4(3 + -2y)
(2 * 45y + -3y * 45y) = 4(3 + -2y)
(90y + -135y2) = 4(3 + -2y)
90y + -135y2 = (3 * 4 + -2y * 4)
90y + -135y2 = (12 + -8y)

Solving
90y + -135y2 = 12 + -8y

Solving for variable 'y'.

Reorder the terms:
-12 + 90y + 8y + -135y2 = 12 + -8y + -12 + 8y

Combine like terms: 90y + 8y = 98y
-12 + 98y + -135y2 = 12 + -8y + -12 + 8y

Reorder the terms:
-12 + 98y + -135y2 = 12 + -12 + -8y + 8y

Combine like terms: 12 + -12 = 0
-12 + 98y + -135y2 = 0 + -8y + 8y
-12 + 98y + -135y2 = -8y + 8y

Combine like terms: -8y + 8y = 0
-12 + 98y + -135y2 = 0

Begin completing the square.  Divide all terms by
-135 the coefficient of the squared term: 

Divide each side by '-135'.
0.08888888889 + -0.7259259259y + y2 = 0

Move the constant term to the right:

Add '-0.08888888889' to each side of the equation.
0.08888888889 + -0.7259259259y + -0.08888888889 + y2 = 0 + -0.08888888889

Reorder the terms:
0.08888888889 + -0.08888888889 + -0.7259259259y + y2 = 0 + -0.08888888889

Combine like terms: 0.08888888889 + -0.08888888889 = 0.00000000000
0.00000000000 + -0.7259259259y + y2 = 0 + -0.08888888889
-0.7259259259y + y2 = 0 + -0.08888888889

Combine like terms: 0 + -0.08888888889 = -0.08888888889
-0.7259259259y + y2 = -0.08888888889

The y term is -0.7259259259y.  Take half its coefficient (-0.362962963).
Square it (0.1317421125) and add it to both sides.

Add '0.1317421125' to each side of the equation.
-0.7259259259y + 0.1317421125 + y2 = -0.08888888889 + 0.1317421125

Reorder the terms:
0.1317421125 + -0.7259259259y + y2 = -0.08888888889 + 0.1317421125

Combine like terms: -0.08888888889 + 0.1317421125 = 0.04285322361
0.1317421125 + -0.7259259259y + y2 = 0.04285322361

Factor a perfect square on the left side:
(y + -0.362962963)(y + -0.362962963) = 0.04285322361

Calculate the square root of the right side: 0.207010202

Break this problem into two subproblems by setting 
(y + -0.362962963) equal to 0.207010202 and -0.207010202.

Subproblem 1
y + -0.362962963 = 0.207010202

Simplifying
y + -0.362962963 = 0.207010202

Reorder the terms:
-0.362962963 + y = 0.207010202

Solving
-0.362962963 + y = 0.207010202

Solving for variable 'y'.

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

Add '0.362962963' to each side of the equation.
-0.362962963 + 0.362962963 + y = 0.207010202 + 0.362962963

Combine like terms: -0.362962963 + 0.362962963 = 0.000000000
0.000000000 + y = 0.207010202 + 0.362962963
y = 0.207010202 + 0.362962963

Combine like terms: 0.207010202 + 0.362962963 = 0.569973165
y = 0.569973165

Simplifying
y = 0.569973165

Subproblem 2
y + -0.362962963 = -0.207010202

Simplifying
y + -0.362962963 = -0.207010202

Reorder the terms:
-0.362962963 + y = -0.207010202

Solving
-0.362962963 + y = -0.207010202

Solving for variable 'y'.

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

Add '0.362962963' to each side of the equation.
-0.362962963 + 0.362962963 + y = -0.207010202 + 0.362962963

Combine like terms: -0.362962963 + 0.362962963 = 0.000000000
0.000000000 + y = -0.207010202 + 0.362962963
y = -0.207010202 + 0.362962963

Combine like terms: -0.207010202 + 0.362962963 = 0.155952761
y = 0.155952761

Simplifying
y = 0.155952761

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.569973165, 0.155952761}