6y*6y=22y+40

Solution for 6y*6y=22y+40 equation:

Simplifying
6y * 6y = 22y + 40

Reorder the terms for easier multiplication:
6 * 6y * y = 22y + 40

Multiply 6 * 6
36y * y = 22y + 40

Multiply y * y
36y2 = 22y + 40

Reorder the terms:
36y2 = 40 + 22y

Solving
36y2 = 40 + 22y

Solving for variable 'y'.

Reorder the terms:
-40 + -22y + 36y2 = 40 + 22y + -40 + -22y

Reorder the terms:
-40 + -22y + 36y2 = 40 + -40 + 22y + -22y

Combine like terms: 40 + -40 = 0
-40 + -22y + 36y2 = 0 + 22y + -22y
-40 + -22y + 36y2 = 22y + -22y

Combine like terms: 22y + -22y = 0
-40 + -22y + 36y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + -11y + 18y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-20 + -11y + 18y2)' equal to zero and attempt to solve:

Simplifying
-20 + -11y + 18y2 = 0

Solving
-20 + -11y + 18y2 = 0

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

Divide each side by '18'.
-1.111111111 + -0.6111111111y + y2 = 0

Move the constant term to the right:

Add '1.111111111' to each side of the equation.
-1.111111111 + -0.6111111111y + 1.111111111 + y2 = 0 + 1.111111111

Reorder the terms:
-1.111111111 + 1.111111111 + -0.6111111111y + y2 = 0 + 1.111111111

Combine like terms: -1.111111111 + 1.111111111 = 0.000000000
0.000000000 + -0.6111111111y + y2 = 0 + 1.111111111
-0.6111111111y + y2 = 0 + 1.111111111

Combine like terms: 0 + 1.111111111 = 1.111111111
-0.6111111111y + y2 = 1.111111111

The y term is -0.6111111111y.  Take half its coefficient (-0.3055555556).
Square it (0.09336419756) and add it to both sides.

Add '0.09336419756' to each side of the equation.
-0.6111111111y + 0.09336419756 + y2 = 1.111111111 + 0.09336419756

Reorder the terms:
0.09336419756 + -0.6111111111y + y2 = 1.111111111 + 0.09336419756

Combine like terms: 1.111111111 + 0.09336419756 = 1.20447530856
0.09336419756 + -0.6111111111y + y2 = 1.20447530856

Factor a perfect square on the left side:
(y + -0.3055555556)(y + -0.3055555556) = 1.20447530856

Calculate the square root of the right side: 1.097485904

Break this problem into two subproblems by setting 
(y + -0.3055555556) equal to 1.097485904 and -1.097485904.

Subproblem 1
y + -0.3055555556 = 1.097485904

Simplifying
y + -0.3055555556 = 1.097485904

Reorder the terms:
-0.3055555556 + y = 1.097485904

Solving
-0.3055555556 + y = 1.097485904

Solving for variable 'y'.

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

Add '0.3055555556' to each side of the equation.
-0.3055555556 + 0.3055555556 + y = 1.097485904 + 0.3055555556

Combine like terms: -0.3055555556 + 0.3055555556 = 0.0000000000
0.0000000000 + y = 1.097485904 + 0.3055555556
y = 1.097485904 + 0.3055555556

Combine like terms: 1.097485904 + 0.3055555556 = 1.4030414596
y = 1.4030414596

Simplifying
y = 1.4030414596

Subproblem 2
y + -0.3055555556 = -1.097485904

Simplifying
y + -0.3055555556 = -1.097485904

Reorder the terms:
-0.3055555556 + y = -1.097485904

Solving
-0.3055555556 + y = -1.097485904

Solving for variable 'y'.

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

Add '0.3055555556' to each side of the equation.
-0.3055555556 + 0.3055555556 + y = -1.097485904 + 0.3055555556

Combine like terms: -0.3055555556 + 0.3055555556 = 0.0000000000
0.0000000000 + y = -1.097485904 + 0.3055555556
y = -1.097485904 + 0.3055555556

Combine like terms: -1.097485904 + 0.3055555556 = -0.7919303484
y = -0.7919303484

Simplifying
y = -0.7919303484

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.4030414596, -0.7919303484}
Solution
y = {1.4030414596, -0.7919303484}