y^2+5y-13=y-1

Solution for y^2+5y-13=y-1 equation:

Simplifying
y2 + 5y + -13 = y + -1

Reorder the terms:
-13 + 5y + y2 = y + -1

Reorder the terms:
-13 + 5y + y2 = -1 + y

Solving
-13 + 5y + y2 = -1 + y

Solving for variable 'y'.

Reorder the terms:
-13 + 1 + 5y + -1y + y2 = -1 + y + 1 + -1y

Combine like terms: -13 + 1 = -12
-12 + 5y + -1y + y2 = -1 + y + 1 + -1y

Combine like terms: 5y + -1y = 4y
-12 + 4y + y2 = -1 + y + 1 + -1y

Reorder the terms:
-12 + 4y + y2 = -1 + 1 + y + -1y

Combine like terms: -1 + 1 = 0
-12 + 4y + y2 = 0 + y + -1y
-12 + 4y + y2 = y + -1y

Combine like terms: y + -1y = 0
-12 + 4y + y2 = 0

Factor a trinomial.
(-6 + -1y)(2 + -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 '(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 = {-6, 2}