-2(-2y+13)3y=-18

Solution for -2(-2y+13)3y=-18 equation:

Simplifying
-2(-2y + 13) * 3y = -18

Reorder the terms:
-2(13 + -2y) * 3y = -18

Reorder the terms for easier multiplication:
-2 * 3y(13 + -2y) = -18

Multiply -2 * 3
-6y(13 + -2y) = -18
(13 * -6y + -2y * -6y) = -18
(-78y + 12y2) = -18

Solving
-78y + 12y2 = -18

Solving for variable 'y'.

Reorder the terms:
18 + -78y + 12y2 = -18 + 18

Combine like terms: -18 + 18 = 0
18 + -78y + 12y2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + -13y + 2y2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(3 + -13y + 2y2)' equal to zero and attempt to solve:

Simplifying
3 + -13y + 2y2 = 0

Solving
3 + -13y + 2y2 = 0

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

Divide each side by '2'.
1.5 + -6.5y + y2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -6.5y + -1.5 + y2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -6.5y + y2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -6.5y + y2 = 0 + -1.5
-6.5y + y2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-6.5y + y2 = -1.5

The y term is -6.5y.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5y + 10.5625 + y2 = -1.5 + 10.5625

Reorder the terms:
10.5625 + -6.5y + y2 = -1.5 + 10.5625

Combine like terms: -1.5 + 10.5625 = 9.0625
10.5625 + -6.5y + y2 = 9.0625

Factor a perfect square on the left side:
(y + -3.25)(y + -3.25) = 9.0625

Calculate the square root of the right side: 3.010398645

Break this problem into two subproblems by setting 
(y + -3.25) equal to 3.010398645 and -3.010398645.

Subproblem 1
y + -3.25 = 3.010398645

Simplifying
y + -3.25 = 3.010398645

Reorder the terms:
-3.25 + y = 3.010398645

Solving
-3.25 + y = 3.010398645

Solving for variable 'y'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + y = 3.010398645 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + y = 3.010398645 + 3.25
y = 3.010398645 + 3.25

Combine like terms: 3.010398645 + 3.25 = 6.260398645
y = 6.260398645

Simplifying
y = 6.260398645

Subproblem 2
y + -3.25 = -3.010398645

Simplifying
y + -3.25 = -3.010398645

Reorder the terms:
-3.25 + y = -3.010398645

Solving
-3.25 + y = -3.010398645

Solving for variable 'y'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + y = -3.010398645 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + y = -3.010398645 + 3.25
y = -3.010398645 + 3.25

Combine like terms: -3.010398645 + 3.25 = 0.239601355
y = 0.239601355

Simplifying
y = 0.239601355

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.260398645, 0.239601355}
Solution
y = {6.260398645, 0.239601355}