-y+14(3y+2)(y+3)=0

Solution for -y+14(3y+2)(y+3)=0 equation:

Simplifying
-1y + 14(3y + 2)(y + 3) = 0

Reorder the terms:
-1y + 14(2 + 3y)(y + 3) = 0

Reorder the terms:
-1y + 14(2 + 3y)(3 + y) = 0

Multiply (2 + 3y) * (3 + y)
-1y + 14(2(3 + y) + 3y * (3 + y)) = 0
-1y + 14((3 * 2 + y * 2) + 3y * (3 + y)) = 0
-1y + 14((6 + 2y) + 3y * (3 + y)) = 0
-1y + 14(6 + 2y + (3 * 3y + y * 3y)) = 0
-1y + 14(6 + 2y + (9y + 3y2)) = 0

Combine like terms: 2y + 9y = 11y
-1y + 14(6 + 11y + 3y2) = 0
-1y + (6 * 14 + 11y * 14 + 3y2 * 14) = 0
-1y + (84 + 154y + 42y2) = 0

Reorder the terms:
84 + -1y + 154y + 42y2 = 0

Combine like terms: -1y + 154y = 153y
84 + 153y + 42y2 = 0

Solving
84 + 153y + 42y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(28 + 51y + 14y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(28 + 51y + 14y2)' equal to zero and attempt to solve:

Simplifying
28 + 51y + 14y2 = 0

Solving
28 + 51y + 14y2 = 0

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

Divide each side by '14'.
2 + 3.642857143y + y2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 3.642857143y + -2 + y2 = 0 + -2

Reorder the terms:
2 + -2 + 3.642857143y + y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3.642857143y + y2 = 0 + -2
3.642857143y + y2 = 0 + -2

Combine like terms: 0 + -2 = -2
3.642857143y + y2 = -2

The y term is 3.642857143y.  Take half its coefficient (1.821428572).
Square it (3.317602043) and add it to both sides.

Add '3.317602043' to each side of the equation.
3.642857143y + 3.317602043 + y2 = -2 + 3.317602043

Reorder the terms:
3.317602043 + 3.642857143y + y2 = -2 + 3.317602043

Combine like terms: -2 + 3.317602043 = 1.317602043
3.317602043 + 3.642857143y + y2 = 1.317602043

Factor a perfect square on the left side:
(y + 1.821428572)(y + 1.821428572) = 1.317602043

Calculate the square root of the right side: 1.147868478

Break this problem into two subproblems by setting 
(y + 1.821428572) equal to 1.147868478 and -1.147868478.

Subproblem 1
y + 1.821428572 = 1.147868478

Simplifying
y + 1.821428572 = 1.147868478

Reorder the terms:
1.821428572 + y = 1.147868478

Solving
1.821428572 + y = 1.147868478

Solving for variable 'y'.

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

Add '-1.821428572' to each side of the equation.
1.821428572 + -1.821428572 + y = 1.147868478 + -1.821428572

Combine like terms: 1.821428572 + -1.821428572 = 0.000000000
0.000000000 + y = 1.147868478 + -1.821428572
y = 1.147868478 + -1.821428572

Combine like terms: 1.147868478 + -1.821428572 = -0.673560094
y = -0.673560094

Simplifying
y = -0.673560094

Subproblem 2
y + 1.821428572 = -1.147868478

Simplifying
y + 1.821428572 = -1.147868478

Reorder the terms:
1.821428572 + y = -1.147868478

Solving
1.821428572 + y = -1.147868478

Solving for variable 'y'.

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

Add '-1.821428572' to each side of the equation.
1.821428572 + -1.821428572 + y = -1.147868478 + -1.821428572

Combine like terms: 1.821428572 + -1.821428572 = 0.000000000
0.000000000 + y = -1.147868478 + -1.821428572
y = -1.147868478 + -1.821428572

Combine like terms: -1.147868478 + -1.821428572 = -2.96929705
y = -2.96929705

Simplifying
y = -2.96929705

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.673560094, -2.96929705}
Solution
y = {-0.673560094, -2.96929705}