y^2-7y+1=-4y-1

Solution for y^2-7y+1=-4y-1 equation:

Simplifying
y2 + -7y + 1 = -4y + -1

Reorder the terms:
1 + -7y + y2 = -4y + -1

Reorder the terms:
1 + -7y + y2 = -1 + -4y

Solving
1 + -7y + y2 = -1 + -4y

Solving for variable 'y'.

Reorder the terms:
1 + 1 + -7y + 4y + y2 = -1 + -4y + 1 + 4y

Combine like terms: 1 + 1 = 2
2 + -7y + 4y + y2 = -1 + -4y + 1 + 4y

Combine like terms: -7y + 4y = -3y
2 + -3y + y2 = -1 + -4y + 1 + 4y

Reorder the terms:
2 + -3y + y2 = -1 + 1 + -4y + 4y

Combine like terms: -1 + 1 = 0
2 + -3y + y2 = 0 + -4y + 4y
2 + -3y + y2 = -4y + 4y

Combine like terms: -4y + 4y = 0
2 + -3y + 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}