y^2-5y-1=-4y+1

Solution for y^2-5y-1=-4y+1 equation:

Simplifying
y2 + -5y + -1 = -4y + 1

Reorder the terms:
-1 + -5y + y2 = -4y + 1

Reorder the terms:
-1 + -5y + y2 = 1 + -4y

Solving
-1 + -5y + y2 = 1 + -4y

Solving for variable 'y'.

Reorder the terms:
-1 + -1 + -5y + 4y + y2 = 1 + -4y + -1 + 4y

Combine like terms: -1 + -1 = -2
-2 + -5y + 4y + y2 = 1 + -4y + -1 + 4y

Combine like terms: -5y + 4y = -1y
-2 + -1y + y2 = 1 + -4y + -1 + 4y

Reorder the terms:
-2 + -1y + y2 = 1 + -1 + -4y + 4y

Combine like terms: 1 + -1 = 0
-2 + -1y + y2 = 0 + -4y + 4y
-2 + -1y + y2 = -4y + 4y

Combine like terms: -4y + 4y = 0
-2 + -1y + y2 = 0

Factor a trinomial.
(-1 + -1y)(2 + -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 '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {-1, 2}