6y^2+33y-213=0

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Solution for 6y^2+33y-213=0 equation: 


Simplifying
6y2 + 33y + -213 = 0

Reorder the terms:
-213 + 33y + 6y2 = 0

Solving
-213 + 33y + 6y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-71 + 11y + 2y2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-71 + 11y + 2y2)' equal to zero and attempt to solve:

Simplifying
-71 + 11y + 2y2 = 0

Solving
-71 + 11y + 2y2 = 0

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

Divide each side by '2'.
-35.5 + 5.5y + y2 = 0

Move the constant term to the right:

Add '35.5' to each side of the equation.
-35.5 + 5.5y + 35.5 + y2 = 0 + 35.5

Reorder the terms:
-35.5 + 35.5 + 5.5y + y2 = 0 + 35.5

Combine like terms: -35.5 + 35.5 = 0.0
0.0 + 5.5y + y2 = 0 + 35.5
5.5y + y2 = 0 + 35.5

Combine like terms: 0 + 35.5 = 35.5
5.5y + y2 = 35.5

The y term is 5.5y.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5y + 7.5625 + y2 = 35.5 + 7.5625

Reorder the terms:
7.5625 + 5.5y + y2 = 35.5 + 7.5625

Combine like terms: 35.5 + 7.5625 = 43.0625
7.5625 + 5.5y + y2 = 43.0625

Factor a perfect square on the left side:
(y + 2.75)(y + 2.75) = 43.0625

Calculate the square root of the right side: 6.562202374

Break this problem into two subproblems by setting 
(y + 2.75) equal to 6.562202374 and -6.562202374.


Subproblem 1
y + 2.75 = 6.562202374

Simplifying
y + 2.75 = 6.562202374

Reorder the terms:
2.75 + y = 6.562202374

Solving
2.75 + y = 6.562202374

Solving for variable 'y'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + y = 6.562202374 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + y = 6.562202374 + -2.75
y = 6.562202374 + -2.75

Combine like terms: 6.562202374 + -2.75 = 3.812202374
y = 3.812202374

Simplifying
y = 3.812202374


Subproblem 2
y + 2.75 = -6.562202374

Simplifying
y + 2.75 = -6.562202374

Reorder the terms:
2.75 + y = -6.562202374

Solving
2.75 + y = -6.562202374

Solving for variable 'y'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + y = -6.562202374 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + y = -6.562202374 + -2.75
y = -6.562202374 + -2.75

Combine like terms: -6.562202374 + -2.75 = -9.312202374
y = -9.312202374

Simplifying
y = -9.312202374


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.812202374, -9.312202374}
Solution
y = {3.812202374, -9.312202374}

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