-2y(3y-1)=-22

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Solution for -2y(3y-1)=-22 equation: 


Simplifying
-2y(3y + -1) = -22

Reorder the terms:
-2y(-1 + 3y) = -22
(-1 * -2y + 3y * -2y) = -22
(2y + -6y2) = -22

Solving
2y + -6y2 = -22

Solving for variable 'y'.

Reorder the terms:
22 + 2y + -6y2 = -22 + 22

Combine like terms: -22 + 22 = 0
22 + 2y + -6y2 = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(11 + y + -3y2)' equal to zero and attempt to solve:

Simplifying
11 + y + -3y2 = 0

Solving
11 + y + -3y2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-3.666666667 + -0.3333333333y + y2 = 0

Move the constant term to the right:

Add '3.666666667' to each side of the equation.
-3.666666667 + -0.3333333333y + 3.666666667 + y2 = 0 + 3.666666667

Reorder the terms:
-3.666666667 + 3.666666667 + -0.3333333333y + y2 = 0 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + -0.3333333333y + y2 = 0 + 3.666666667
-0.3333333333y + y2 = 0 + 3.666666667

Combine like terms: 0 + 3.666666667 = 3.666666667
-0.3333333333y + y2 = 3.666666667

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.3333333333y + 0.25 + y2 = 3.666666667 + 0.25

Reorder the terms:
0.25 + -0.3333333333y + y2 = 3.666666667 + 0.25

Combine like terms: 3.666666667 + 0.25 = 3.916666667
0.25 + -0.3333333333y + y2 = 3.916666667

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 3.916666667

Calculate the square root of the right side: 1.979057015

Break this problem into two subproblems by setting 
(y + 0.5) equal to 1.979057015 and -1.979057015.


Subproblem 1
y + 0.5 = 1.979057015

Simplifying
y + 0.5 = 1.979057015

Reorder the terms:
0.5 + y = 1.979057015

Solving
0.5 + y = 1.979057015

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = 1.979057015 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 1.979057015 + -0.5
y = 1.979057015 + -0.5

Combine like terms: 1.979057015 + -0.5 = 1.479057015
y = 1.479057015

Simplifying
y = 1.479057015


Subproblem 2
y + 0.5 = -1.979057015

Simplifying
y + 0.5 = -1.979057015

Reorder the terms:
0.5 + y = -1.979057015

Solving
0.5 + y = -1.979057015

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = -1.979057015 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -1.979057015 + -0.5
y = -1.979057015 + -0.5

Combine like terms: -1.979057015 + -0.5 = -2.479057015
y = -2.479057015

Simplifying
y = -2.479057015


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.479057015, -2.479057015}
Solution
y = {1.479057015, -2.479057015}

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