3y^2-6y-21=

Solution for 3y^2-6y-21= equation:

Simplifying
3y2 + -6y + -21 = 0

Reorder the terms:
-21 + -6y + 3y2 = 0

Solving
-21 + -6y + 3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + -2y + y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-7 + -2y + y2)' equal to zero and attempt to solve:

Simplifying
-7 + -2y + y2 = 0

Solving
-7 + -2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -2y + 7 + y2 = 0 + 7

Reorder the terms:
-7 + 7 + -2y + y2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2y + y2 = 0 + 7
-2y + y2 = 0 + 7

Combine like terms: 0 + 7 = 7
-2y + y2 = 7

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 = 7 + 1

Reorder the terms:
1 + -2y + y2 = 7 + 1

Combine like terms: 7 + 1 = 8
1 + -2y + y2 = 8

Factor a perfect square on the left side:
(y + -1)(y + -1) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(y + -1) equal to 2.828427125 and -2.828427125.

Subproblem 1
y + -1 = 2.828427125

Simplifying
y + -1 = 2.828427125

Reorder the terms:
-1 + y = 2.828427125

Solving
-1 + y = 2.828427125

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 = 2.828427125 + 1

Combine like terms: -1 + 1 = 0
0 + y = 2.828427125 + 1
y = 2.828427125 + 1

Combine like terms: 2.828427125 + 1 = 3.828427125
y = 3.828427125

Simplifying
y = 3.828427125

Subproblem 2
y + -1 = -2.828427125

Simplifying
y + -1 = -2.828427125

Reorder the terms:
-1 + y = -2.828427125

Solving
-1 + y = -2.828427125

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 = -2.828427125 + 1

Combine like terms: -1 + 1 = 0
0 + y = -2.828427125 + 1
y = -2.828427125 + 1

Combine like terms: -2.828427125 + 1 = -1.828427125
y = -1.828427125

Simplifying
y = -1.828427125

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.828427125, -1.828427125}
Solution
y = {3.828427125, -1.828427125}