y^2-y=-6y+6

Solution for y^2-y=-6y+6 equation:

Simplifying
y2 + -1y = -6y + 6

Reorder the terms:
-1y + y2 = -6y + 6

Reorder the terms:
-1y + y2 = 6 + -6y

Solving
-1y + y2 = 6 + -6y

Solving for variable 'y'.

Reorder the terms:
-6 + -1y + 6y + y2 = 6 + -6y + -6 + 6y

Combine like terms: -1y + 6y = 5y
-6 + 5y + y2 = 6 + -6y + -6 + 6y

Reorder the terms:
-6 + 5y + y2 = 6 + -6 + -6y + 6y

Combine like terms: 6 + -6 = 0
-6 + 5y + y2 = 0 + -6y + 6y
-6 + 5y + y2 = -6y + 6y

Combine like terms: -6y + 6y = 0
-6 + 5y + y2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
y = {-6, 1}