6y*6y+9y-6=0

Solution for 6y*6y+9y-6=0 equation:

Simplifying
6y * 6y + 9y + -6 = 0

Reorder the terms for easier multiplication:
6 * 6y * y + 9y + -6 = 0

Multiply 6 * 6
36y * y + 9y + -6 = 0

Multiply y * y
36y2 + 9y + -6 = 0

Reorder the terms:
-6 + 9y + 36y2 = 0

Solving
-6 + 9y + 36y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 3y + 12y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + 3y + 12y2)' equal to zero and attempt to solve:

Simplifying
-2 + 3y + 12y2 = 0

Solving
-2 + 3y + 12y2 = 0

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

Divide each side by '12'.
-0.1666666667 + 0.25y + y2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.25y + 0.1666666667 + y2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + 0.25y + y2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + 0.25y + y2 = 0 + 0.1666666667
0.25y + y2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
0.25y + y2 = 0.1666666667

The y term is 0.25y.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25y + 0.015625 + y2 = 0.1666666667 + 0.015625

Reorder the terms:
0.015625 + 0.25y + y2 = 0.1666666667 + 0.015625

Combine like terms: 0.1666666667 + 0.015625 = 0.1822916667
0.015625 + 0.25y + y2 = 0.1822916667

Factor a perfect square on the left side:
(y + 0.125)(y + 0.125) = 0.1822916667

Calculate the square root of the right side: 0.426956282

Break this problem into two subproblems by setting 
(y + 0.125) equal to 0.426956282 and -0.426956282.

Subproblem 1
y + 0.125 = 0.426956282

Simplifying
y + 0.125 = 0.426956282

Reorder the terms:
0.125 + y = 0.426956282

Solving
0.125 + y = 0.426956282

Solving for variable 'y'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + y = 0.426956282 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + y = 0.426956282 + -0.125
y = 0.426956282 + -0.125

Combine like terms: 0.426956282 + -0.125 = 0.301956282
y = 0.301956282

Simplifying
y = 0.301956282

Subproblem 2
y + 0.125 = -0.426956282

Simplifying
y + 0.125 = -0.426956282

Reorder the terms:
0.125 + y = -0.426956282

Solving
0.125 + y = -0.426956282

Solving for variable 'y'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + y = -0.426956282 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + y = -0.426956282 + -0.125
y = -0.426956282 + -0.125

Combine like terms: -0.426956282 + -0.125 = -0.551956282
y = -0.551956282

Simplifying
y = -0.551956282

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.301956282, -0.551956282}
Solution
y = {0.301956282, -0.551956282}