(y-6)(y+7)=

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

Simplifying
(y + -6)(y + 7) = 0

Reorder the terms:
(-6 + y)(y + 7) = 0

Reorder the terms:
(-6 + y)(7 + y) = 0

Multiply (-6 + y) * (7 + y)
(-6(7 + y) + y(7 + y)) = 0
((7 * -6 + y * -6) + y(7 + y)) = 0
((-42 + -6y) + y(7 + y)) = 0
(-42 + -6y + (7 * y + y * y)) = 0
(-42 + -6y + (7y + y2)) = 0

Combine like terms: -6y + 7y = 1y
(-42 + 1y + y2) = 0

Solving
-42 + 1y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-7 + -1y)(6 + -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 '(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
Solution
y = {-7, 6}