y(y-7)-6=2

Solution for y(y-7)-6=2 equation:

Simplifying
y(y + -7) + -6 = 2

Reorder the terms:
y(-7 + y) + -6 = 2
(-7 * y + y * y) + -6 = 2
(-7y + y2) + -6 = 2

Reorder the terms:
-6 + -7y + y2 = 2

Solving
-6 + -7y + y2 = 2

Solving for variable 'y'.

Reorder the terms:
-6 + -2 + -7y + y2 = 2 + -2

Combine like terms: -6 + -2 = -8
-8 + -7y + y2 = 2 + -2

Combine like terms: 2 + -2 = 0
-8 + -7y + y2 = 0

Factor a trinomial.
(-1 + -1y)(8 + -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 '(8 + -1y)' equal to zero and attempt to solve:

Simplifying
8 + -1y = 0

Solving
8 + -1y = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1y = 0 + -8
-1y = 0 + -8

Combine like terms: 0 + -8 = -8
-1y = -8

Divide each side by '-1'.
y = 8

Simplifying
y = 8
Solution
y = {-1, 8}