6y*2=(2y*2y)-6

Solution for 6y*2=(2y*2y)-6 equation:

Simplifying
6y * 2 = (2y * 2y) + -6

Reorder the terms for easier multiplication:
6 * 2y = (2y * 2y) + -6

Multiply 6 * 2
12y = (2y * 2y) + -6

Reorder the terms for easier multiplication:
12y = (2 * 2y * y) + -6

Multiply 2 * 2
12y = (4y * y) + -6

Multiply y * y
12y = (4y2) + -6

Reorder the terms:
12y = -6 + (4y2)

Solving
12y = -6 + (4y2)

Solving for variable 'y'.

Reorder the terms:
6 + 12y + (-4y2) = -6 + (4y2) + 6 + (-4y2)

Reorder the terms:
6 + 12y + (-4y2) = -6 + 6 + (4y2) + (-4y2)

Combine like terms: -6 + 6 = 0
6 + 12y + (-4y2) = 0 + (4y2) + (-4y2)
6 + 12y + (-4y2) = (4y2) + (-4y2)

Combine like terms: (4y2) + (-4y2) = 0
6 + 12y + (-4y2) = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 6y + (-2y2)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 6y + (-2y2))' equal to zero and attempt to solve:

Simplifying
3 + 6y + (-2y2) = 0

Solving
3 + 6y + (-2y2) = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-1.5 + -3y + y2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -3y + 1.5 + y2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -3y + y2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -3y + y2 = 0 + 1.5
-3y + y2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-3y + y2 = 1.5

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = 1.5 + 2.25

Reorder the terms:
2.25 + -3y + y2 = 1.5 + 2.25

Combine like terms: 1.5 + 2.25 = 3.75
2.25 + -3y + y2 = 3.75

Factor a perfect square on the left side:
((y) + -1.5)((y) + -1.5) = 3.75

Calculate the square root of the right side: 1.936491673

Break this problem into two subproblems by setting 
((y) + -1.5) equal to 1.936491673 and -1.936491673.

Subproblem 1
(y) + -1.5 = 1.936491673

Simplifying
(y) + -1.5 = 1.936491673
y + -1.5 = 1.936491673

Reorder the terms:
-1.5 + y = 1.936491673

Solving
-1.5 + y = 1.936491673

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = 1.936491673 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 1.936491673 + 1.5
y = 1.936491673 + 1.5

Combine like terms: 1.936491673 + 1.5 = 3.436491673
y = 3.436491673

Simplifying
y = 3.436491673

Subproblem 2
(y) + -1.5 = -1.936491673

Simplifying
(y) + -1.5 = -1.936491673
y + -1.5 = -1.936491673

Reorder the terms:
-1.5 + y = -1.936491673

Solving
-1.5 + y = -1.936491673

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = -1.936491673 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -1.936491673 + 1.5
y = -1.936491673 + 1.5

Combine like terms: -1.936491673 + 1.5 = -0.436491673
y = -0.436491673

Simplifying
y = -0.436491673

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.436491673, -0.436491673}
Solution
y = {3.436491673, -0.436491673}