y^2-10y+9=-3y-3

Solution for y^2-10y+9=-3y-3 equation:

Simplifying
y2 + -10y + 9 = -3y + -3

Reorder the terms:
9 + -10y + y2 = -3y + -3

Reorder the terms:
9 + -10y + y2 = -3 + -3y

Solving
9 + -10y + y2 = -3 + -3y

Solving for variable 'y'.

Reorder the terms:
9 + 3 + -10y + 3y + y2 = -3 + -3y + 3 + 3y

Combine like terms: 9 + 3 = 12
12 + -10y + 3y + y2 = -3 + -3y + 3 + 3y

Combine like terms: -10y + 3y = -7y
12 + -7y + y2 = -3 + -3y + 3 + 3y

Reorder the terms:
12 + -7y + y2 = -3 + 3 + -3y + 3y

Combine like terms: -3 + 3 = 0
12 + -7y + y2 = 0 + -3y + 3y
12 + -7y + y2 = -3y + 3y

Combine like terms: -3y + 3y = 0
12 + -7y + y2 = 0

Factor a trinomial.
(3 + -1y)(4 + -1y) = 0

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

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Subproblem 2
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {3, 4}