y^2-7y=y+9

Solution for y^2-7y=y+9 equation:

Simplifying
y2 + -7y = y + 9

Reorder the terms:
-7y + y2 = y + 9

Reorder the terms:
-7y + y2 = 9 + y

Solving
-7y + y2 = 9 + y

Solving for variable 'y'.

Reorder the terms:
-9 + -7y + -1y + y2 = 9 + y + -9 + -1y

Combine like terms: -7y + -1y = -8y
-9 + -8y + y2 = 9 + y + -9 + -1y

Reorder the terms:
-9 + -8y + y2 = 9 + -9 + y + -1y

Combine like terms: 9 + -9 = 0
-9 + -8y + y2 = 0 + y + -1y
-9 + -8y + y2 = y + -1y

Combine like terms: y + -1y = 0
-9 + -8y + y2 = 0

Factor a trinomial.
(-1 + -1y)(9 + -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 '(9 + -1y)' equal to zero and attempt to solve:

Simplifying
9 + -1y = 0

Solving
9 + -1y = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1y = 0 + -9
-1y = 0 + -9

Combine like terms: 0 + -9 = -9
-1y = -9

Divide each side by '-1'.
y = 9

Simplifying
y = 9
Solution
y = {-1, 9}