(y-1)(y+6)-8=0

Solution for (y-1)(y+6)-8=0 equation:

Simplifying
(y + -1)(y + 6) + -8 = 0

Reorder the terms:
(-1 + y)(y + 6) + -8 = 0

Reorder the terms:
(-1 + y)(6 + y) + -8 = 0

Multiply (-1 + y) * (6 + y)
(-1(6 + y) + y(6 + y)) + -8 = 0
((6 * -1 + y * -1) + y(6 + y)) + -8 = 0
((-6 + -1y) + y(6 + y)) + -8 = 0
(-6 + -1y + (6 * y + y * y)) + -8 = 0
(-6 + -1y + (6y + y2)) + -8 = 0

Combine like terms: -1y + 6y = 5y
(-6 + 5y + y2) + -8 = 0

Reorder the terms:
-6 + -8 + 5y + y2 = 0

Combine like terms: -6 + -8 = -14
-14 + 5y + y2 = 0

Solving
-14 + 5y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-7 + -1y)(2 + -1y) = 0

Subproblem 1
Set the factor '(-7 + -1y)' equal to zero and attempt to solve:

Simplifying
-7 + -1y = 0

Solving
-7 + -1y = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1y = 0 + 7
-1y = 0 + 7

Combine like terms: 0 + 7 = 7
-1y = 7

Divide each side by '-1'.
y = -7

Simplifying
y = -7
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 = {-7, 2}