3y^2-6y-42=0

Solution for 3y^2-6y-42=0 equation:

Simplifying
3y2 + -6y + -42 = 0

Reorder the terms:
-42 + -6y + 3y2 = 0

Solving
-42 + -6y + 3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + -2y + y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-14 + -2y + y2)' equal to zero and attempt to solve:

Simplifying
-14 + -2y + y2 = 0

Solving
-14 + -2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -2y + 14 + y2 = 0 + 14

Reorder the terms:
-14 + 14 + -2y + y2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -2y + y2 = 0 + 14
-2y + y2 = 0 + 14

Combine like terms: 0 + 14 = 14
-2y + y2 = 14

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = 14 + 1

Reorder the terms:
1 + -2y + y2 = 14 + 1

Combine like terms: 14 + 1 = 15
1 + -2y + y2 = 15

Factor a perfect square on the left side:
(y + -1)(y + -1) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(y + -1) equal to 3.872983346 and -3.872983346.

Subproblem 1
y + -1 = 3.872983346

Simplifying
y + -1 = 3.872983346

Reorder the terms:
-1 + y = 3.872983346

Solving
-1 + y = 3.872983346

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = 3.872983346 + 1

Combine like terms: -1 + 1 = 0
0 + y = 3.872983346 + 1
y = 3.872983346 + 1

Combine like terms: 3.872983346 + 1 = 4.872983346
y = 4.872983346

Simplifying
y = 4.872983346

Subproblem 2
y + -1 = -3.872983346

Simplifying
y + -1 = -3.872983346

Reorder the terms:
-1 + y = -3.872983346

Solving
-1 + y = -3.872983346

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = -3.872983346 + 1

Combine like terms: -1 + 1 = 0
0 + y = -3.872983346 + 1
y = -3.872983346 + 1

Combine like terms: -3.872983346 + 1 = -2.872983346
y = -2.872983346

Simplifying
y = -2.872983346

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.872983346, -2.872983346}
Solution
y = {4.872983346, -2.872983346}