9y(y-7)+2(3y-9)=

Solution for 9y(y-7)+2(3y-9)= equation:

Simplifying
9y(y + -7) + 2(3y + -9) = 0

Reorder the terms:
9y(-7 + y) + 2(3y + -9) = 0
(-7 * 9y + y * 9y) + 2(3y + -9) = 0
(-63y + 9y2) + 2(3y + -9) = 0

Reorder the terms:
-63y + 9y2 + 2(-9 + 3y) = 0
-63y + 9y2 + (-9 * 2 + 3y * 2) = 0
-63y + 9y2 + (-18 + 6y) = 0

Reorder the terms:
-18 + -63y + 6y + 9y2 = 0

Combine like terms: -63y + 6y = -57y
-18 + -57y + 9y2 = 0

Solving
-18 + -57y + 9y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + -19y + 3y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + -19y + 3y2)' equal to zero and attempt to solve:

Simplifying
-6 + -19y + 3y2 = 0

Solving
-6 + -19y + 3y2 = 0

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

Divide each side by '3'.
-2 + -6.333333333y + y2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -6.333333333y + 2 + y2 = 0 + 2

Reorder the terms:
-2 + 2 + -6.333333333y + y2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -6.333333333y + y2 = 0 + 2
-6.333333333y + y2 = 0 + 2

Combine like terms: 0 + 2 = 2
-6.333333333y + y2 = 2

The y term is -6.333333333y.  Take half its coefficient (-3.166666667).
Square it (10.02777778) and add it to both sides.

Add '10.02777778' to each side of the equation.
-6.333333333y + 10.02777778 + y2 = 2 + 10.02777778

Reorder the terms:
10.02777778 + -6.333333333y + y2 = 2 + 10.02777778

Combine like terms: 2 + 10.02777778 = 12.02777778
10.02777778 + -6.333333333y + y2 = 12.02777778

Factor a perfect square on the left side:
(y + -3.166666667)(y + -3.166666667) = 12.02777778

Calculate the square root of the right side: 3.468108675

Break this problem into two subproblems by setting 
(y + -3.166666667) equal to 3.468108675 and -3.468108675.

Subproblem 1
y + -3.166666667 = 3.468108675

Simplifying
y + -3.166666667 = 3.468108675

Reorder the terms:
-3.166666667 + y = 3.468108675

Solving
-3.166666667 + y = 3.468108675

Solving for variable 'y'.

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

Add '3.166666667' to each side of the equation.
-3.166666667 + 3.166666667 + y = 3.468108675 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + y = 3.468108675 + 3.166666667
y = 3.468108675 + 3.166666667

Combine like terms: 3.468108675 + 3.166666667 = 6.634775342
y = 6.634775342

Simplifying
y = 6.634775342

Subproblem 2
y + -3.166666667 = -3.468108675

Simplifying
y + -3.166666667 = -3.468108675

Reorder the terms:
-3.166666667 + y = -3.468108675

Solving
-3.166666667 + y = -3.468108675

Solving for variable 'y'.

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

Add '3.166666667' to each side of the equation.
-3.166666667 + 3.166666667 + y = -3.468108675 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + y = -3.468108675 + 3.166666667
y = -3.468108675 + 3.166666667

Combine like terms: -3.468108675 + 3.166666667 = -0.301442008
y = -0.301442008

Simplifying
y = -0.301442008

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.634775342, -0.301442008}
Solution
y = {6.634775342, -0.301442008}