6+2(5y-2)=-3(3y-2)9y

Solution for 6+2(5y-2)=-3(3y-2)9y equation:

Simplifying
6 + 2(5y + -2) = -3(3y + -2) * 9y

Reorder the terms:
6 + 2(-2 + 5y) = -3(3y + -2) * 9y
6 + (-2 * 2 + 5y * 2) = -3(3y + -2) * 9y
6 + (-4 + 10y) = -3(3y + -2) * 9y

Combine like terms: 6 + -4 = 2
2 + 10y = -3(3y + -2) * 9y

Reorder the terms:
2 + 10y = -3(-2 + 3y) * 9y

Reorder the terms for easier multiplication:
2 + 10y = -3 * 9y(-2 + 3y)

Multiply -3 * 9
2 + 10y = -27y(-2 + 3y)
2 + 10y = (-2 * -27y + 3y * -27y)
2 + 10y = (54y + -81y2)

Solving
2 + 10y = 54y + -81y2

Solving for variable 'y'.

Combine like terms: 10y + -54y = -44y
2 + -44y + 81y2 = 54y + -81y2 + -54y + 81y2

Reorder the terms:
2 + -44y + 81y2 = 54y + -54y + -81y2 + 81y2

Combine like terms: 54y + -54y = 0
2 + -44y + 81y2 = 0 + -81y2 + 81y2
2 + -44y + 81y2 = -81y2 + 81y2

Combine like terms: -81y2 + 81y2 = 0
2 + -44y + 81y2 = 0

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

Divide each side by '81'.
0.02469135802 + -0.5432098765y + y2 = 0

Move the constant term to the right:

Add '-0.02469135802' to each side of the equation.
0.02469135802 + -0.5432098765y + -0.02469135802 + y2 = 0 + -0.02469135802

Reorder the terms:
0.02469135802 + -0.02469135802 + -0.5432098765y + y2 = 0 + -0.02469135802

Combine like terms: 0.02469135802 + -0.02469135802 = 0.00000000000
0.00000000000 + -0.5432098765y + y2 = 0 + -0.02469135802
-0.5432098765y + y2 = 0 + -0.02469135802

Combine like terms: 0 + -0.02469135802 = -0.02469135802
-0.5432098765y + y2 = -0.02469135802

The y term is -0.5432098765y.  Take half its coefficient (-0.2716049383).
Square it (0.07376924251) and add it to both sides.

Add '0.07376924251' to each side of the equation.
-0.5432098765y + 0.07376924251 + y2 = -0.02469135802 + 0.07376924251

Reorder the terms:
0.07376924251 + -0.5432098765y + y2 = -0.02469135802 + 0.07376924251

Combine like terms: -0.02469135802 + 0.07376924251 = 0.04907788449
0.07376924251 + -0.5432098765y + y2 = 0.04907788449

Factor a perfect square on the left side:
(y + -0.2716049383)(y + -0.2716049383) = 0.04907788449

Calculate the square root of the right side: 0.221535289

Break this problem into two subproblems by setting 
(y + -0.2716049383) equal to 0.221535289 and -0.221535289.

Subproblem 1
y + -0.2716049383 = 0.221535289

Simplifying
y + -0.2716049383 = 0.221535289

Reorder the terms:
-0.2716049383 + y = 0.221535289

Solving
-0.2716049383 + y = 0.221535289

Solving for variable 'y'.

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

Add '0.2716049383' to each side of the equation.
-0.2716049383 + 0.2716049383 + y = 0.221535289 + 0.2716049383

Combine like terms: -0.2716049383 + 0.2716049383 = 0.0000000000
0.0000000000 + y = 0.221535289 + 0.2716049383
y = 0.221535289 + 0.2716049383

Combine like terms: 0.221535289 + 0.2716049383 = 0.4931402273
y = 0.4931402273

Simplifying
y = 0.4931402273

Subproblem 2
y + -0.2716049383 = -0.221535289

Simplifying
y + -0.2716049383 = -0.221535289

Reorder the terms:
-0.2716049383 + y = -0.221535289

Solving
-0.2716049383 + y = -0.221535289

Solving for variable 'y'.

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

Add '0.2716049383' to each side of the equation.
-0.2716049383 + 0.2716049383 + y = -0.221535289 + 0.2716049383

Combine like terms: -0.2716049383 + 0.2716049383 = 0.0000000000
0.0000000000 + y = -0.221535289 + 0.2716049383
y = -0.221535289 + 0.2716049383

Combine like terms: -0.221535289 + 0.2716049383 = 0.0500696493
y = 0.0500696493

Simplifying
y = 0.0500696493

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.4931402273, 0.0500696493}