7(2y^2-9y)+5y(9-2y+3y^2)=

Solution for 7(2y^2-9y)+5y(9-2y+3y^2)= equation:

Simplifying
7(2y2 + -9y) + 5y(9 + -2y + 3y2) = 0

Reorder the terms:
7(-9y + 2y2) + 5y(9 + -2y + 3y2) = 0
(-9y * 7 + 2y2 * 7) + 5y(9 + -2y + 3y2) = 0
(-63y + 14y2) + 5y(9 + -2y + 3y2) = 0
-63y + 14y2 + (9 * 5y + -2y * 5y + 3y2 * 5y) = 0
-63y + 14y2 + (45y + -10y2 + 15y3) = 0

Reorder the terms:
-63y + 45y + 14y2 + -10y2 + 15y3 = 0

Combine like terms: -63y + 45y = -18y
-18y + 14y2 + -10y2 + 15y3 = 0

Combine like terms: 14y2 + -10y2 = 4y2
-18y + 4y2 + 15y3 = 0

Solving
-18y + 4y2 + 15y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-18 + 4y + 15y2) = 0

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(-18 + 4y + 15y2)' equal to zero and attempt to solve:

Simplifying
-18 + 4y + 15y2 = 0

Solving
-18 + 4y + 15y2 = 0

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

Divide each side by '15'.
-1.2 + 0.2666666667y + y2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + 0.2666666667y + 1.2 + y2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + 0.2666666667y + y2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + 0.2666666667y + y2 = 0 + 1.2
0.2666666667y + y2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
0.2666666667y + y2 = 1.2

The y term is 0.2666666667y.  Take half its coefficient (0.1333333334).
Square it (0.01777777780) and add it to both sides.

Add '0.01777777780' to each side of the equation.
0.2666666667y + 0.01777777780 + y2 = 1.2 + 0.01777777780

Reorder the terms:
0.01777777780 + 0.2666666667y + y2 = 1.2 + 0.01777777780

Combine like terms: 1.2 + 0.01777777780 = 1.2177777778
0.01777777780 + 0.2666666667y + y2 = 1.2177777778

Factor a perfect square on the left side:
(y + 0.1333333334)(y + 0.1333333334) = 1.2177777778

Calculate the square root of the right side: 1.10352969

Break this problem into two subproblems by setting 
(y + 0.1333333334) equal to 1.10352969 and -1.10352969.

Subproblem 1
y + 0.1333333334 = 1.10352969

Simplifying
y + 0.1333333334 = 1.10352969

Reorder the terms:
0.1333333334 + y = 1.10352969

Solving
0.1333333334 + y = 1.10352969

Solving for variable 'y'.

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

Add '-0.1333333334' to each side of the equation.
0.1333333334 + -0.1333333334 + y = 1.10352969 + -0.1333333334

Combine like terms: 0.1333333334 + -0.1333333334 = 0.0000000000
0.0000000000 + y = 1.10352969 + -0.1333333334
y = 1.10352969 + -0.1333333334

Combine like terms: 1.10352969 + -0.1333333334 = 0.9701963566
y = 0.9701963566

Simplifying
y = 0.9701963566

Subproblem 2
y + 0.1333333334 = -1.10352969

Simplifying
y + 0.1333333334 = -1.10352969

Reorder the terms:
0.1333333334 + y = -1.10352969

Solving
0.1333333334 + y = -1.10352969

Solving for variable 'y'.

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

Add '-0.1333333334' to each side of the equation.
0.1333333334 + -0.1333333334 + y = -1.10352969 + -0.1333333334

Combine like terms: 0.1333333334 + -0.1333333334 = 0.0000000000
0.0000000000 + y = -1.10352969 + -0.1333333334
y = -1.10352969 + -0.1333333334

Combine like terms: -1.10352969 + -0.1333333334 = -1.2368630234
y = -1.2368630234

Simplifying
y = -1.2368630234

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.9701963566, -1.2368630234}
Solution
y = {0, 0.9701963566, -1.2368630234}