(y-7)(y+6)=

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

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

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

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

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

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

Solving
-42 + -1y + y2 = 0

Solving for variable 'y'.

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