-8y*3(y+3)=-14

Solution for -8y*3(y+3)=-14 equation:

Simplifying
-8y * 3(y + 3) = -14

Reorder the terms:
-8y * 3(3 + y) = -14

Reorder the terms for easier multiplication:
-8 * 3y(3 + y) = -14

Multiply -8 * 3
-24y(3 + y) = -14
(3 * -24y + y * -24y) = -14
(-72y + -24y2) = -14

Solving
-72y + -24y2 = -14

Solving for variable 'y'.

Reorder the terms:
14 + -72y + -24y2 = -14 + 14

Combine like terms: -14 + 14 = 0
14 + -72y + -24y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -36y + -12y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + -36y + -12y2)' equal to zero and attempt to solve:

Simplifying
7 + -36y + -12y2 = 0

Solving
7 + -36y + -12y2 = 0

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

Divide each side by '-12'.
-0.5833333333 + 3y + y2 = 0

Move the constant term to the right:

Add '0.5833333333' to each side of the equation.
-0.5833333333 + 3y + 0.5833333333 + y2 = 0 + 0.5833333333

Reorder the terms:
-0.5833333333 + 0.5833333333 + 3y + y2 = 0 + 0.5833333333

Combine like terms: -0.5833333333 + 0.5833333333 = 0.0000000000
0.0000000000 + 3y + y2 = 0 + 0.5833333333
3y + y2 = 0 + 0.5833333333

Combine like terms: 0 + 0.5833333333 = 0.5833333333
3y + y2 = 0.5833333333

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 = 0.5833333333 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 0.5833333333 + 2.25

Combine like terms: 0.5833333333 + 2.25 = 2.8333333333
2.25 + 3y + y2 = 2.8333333333

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 2.8333333333

Calculate the square root of the right side: 1.683250823

Break this problem into two subproblems by setting 
(y + 1.5) equal to 1.683250823 and -1.683250823.

Subproblem 1
y + 1.5 = 1.683250823

Simplifying
y + 1.5 = 1.683250823

Reorder the terms:
1.5 + y = 1.683250823

Solving
1.5 + y = 1.683250823

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 = 1.683250823 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = 1.683250823 + -1.5
y = 1.683250823 + -1.5

Combine like terms: 1.683250823 + -1.5 = 0.183250823
y = 0.183250823

Simplifying
y = 0.183250823

Subproblem 2
y + 1.5 = -1.683250823

Simplifying
y + 1.5 = -1.683250823

Reorder the terms:
1.5 + y = -1.683250823

Solving
1.5 + y = -1.683250823

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 = -1.683250823 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = -1.683250823 + -1.5
y = -1.683250823 + -1.5

Combine like terms: -1.683250823 + -1.5 = -3.183250823
y = -3.183250823

Simplifying
y = -3.183250823

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.183250823, -3.183250823}
Solution
y = {0.183250823, -3.183250823}