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

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

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

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

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

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

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

Solving
-6 + 5y + y2 = 8

Solving for variable 'y'.

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

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

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

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}