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

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

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

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

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

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

Solving for variable 'y'.

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

Combine like terms: 3 + 3 = 6
6 + -10y + 3y + y2 = -3 + -3y + 3 + 3y

Combine like terms: -10y + 3y = -7y
6 + -7y + y2 = -3 + -3y + 3 + 3y

Reorder the terms:
6 + -7y + y2 = -3 + 3 + -3y + 3y

Combine like terms: -3 + 3 = 0
6 + -7y + y2 = 0 + -3y + 3y
6 + -7y + y2 = -3y + 3y

Combine like terms: -3y + 3y = 0
6 + -7y + y2 = 0

Factor a trinomial.
(1 + -1y)(6 + -1y) = 0

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

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

Simplifying
y = 1
Subproblem 2
Set the factor '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Solution
y = {1, 6}