-9(y-5)-10=-3y(y-5)

Solution for -9(y-5)-10=-3y(y-5) equation:

Simplifying
-9(y + -5) + -10 = -3y(y + -5)

Reorder the terms:
-9(-5 + y) + -10 = -3y(y + -5)
(-5 * -9 + y * -9) + -10 = -3y(y + -5)
(45 + -9y) + -10 = -3y(y + -5)

Reorder the terms:
45 + -10 + -9y = -3y(y + -5)

Combine like terms: 45 + -10 = 35
35 + -9y = -3y(y + -5)

Reorder the terms:
35 + -9y = -3y(-5 + y)
35 + -9y = (-5 * -3y + y * -3y)
35 + -9y = (15y + -3y2)

Solving
35 + -9y = 15y + -3y2

Solving for variable 'y'.

Combine like terms: -9y + -15y = -24y
35 + -24y + 3y2 = 15y + -3y2 + -15y + 3y2

Reorder the terms:
35 + -24y + 3y2 = 15y + -15y + -3y2 + 3y2

Combine like terms: 15y + -15y = 0
35 + -24y + 3y2 = 0 + -3y2 + 3y2
35 + -24y + 3y2 = -3y2 + 3y2

Combine like terms: -3y2 + 3y2 = 0
35 + -24y + 3y2 = 0

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

Divide each side by '3'.
11.66666667 + -8y + y2 = 0

Move the constant term to the right:

Add '-11.66666667' to each side of the equation.
11.66666667 + -8y + -11.66666667 + y2 = 0 + -11.66666667

Reorder the terms:
11.66666667 + -11.66666667 + -8y + y2 = 0 + -11.66666667

Combine like terms: 11.66666667 + -11.66666667 = 0.00000000
0.00000000 + -8y + y2 = 0 + -11.66666667
-8y + y2 = 0 + -11.66666667

Combine like terms: 0 + -11.66666667 = -11.66666667
-8y + y2 = -11.66666667

The y term is -8y.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8y + 16 + y2 = -11.66666667 + 16

Reorder the terms:
16 + -8y + y2 = -11.66666667 + 16

Combine like terms: -11.66666667 + 16 = 4.33333333
16 + -8y + y2 = 4.33333333

Factor a perfect square on the left side:
(y + -4)(y + -4) = 4.33333333

Calculate the square root of the right side: 2.081665999

Break this problem into two subproblems by setting 
(y + -4) equal to 2.081665999 and -2.081665999.

Subproblem 1
y + -4 = 2.081665999

Simplifying
y + -4 = 2.081665999

Reorder the terms:
-4 + y = 2.081665999

Solving
-4 + y = 2.081665999

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = 2.081665999 + 4

Combine like terms: -4 + 4 = 0
0 + y = 2.081665999 + 4
y = 2.081665999 + 4

Combine like terms: 2.081665999 + 4 = 6.081665999
y = 6.081665999

Simplifying
y = 6.081665999

Subproblem 2
y + -4 = -2.081665999

Simplifying
y + -4 = -2.081665999

Reorder the terms:
-4 + y = -2.081665999

Solving
-4 + y = -2.081665999

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = -2.081665999 + 4

Combine like terms: -4 + 4 = 0
0 + y = -2.081665999 + 4
y = -2.081665999 + 4

Combine like terms: -2.081665999 + 4 = 1.918334001
y = 1.918334001

Simplifying
y = 1.918334001

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.081665999, 1.918334001}