(v-7)(v+6)=0

Solution for (v-7)(v+6)=0 equation:

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

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

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

Multiply (-7 + v) * (6 + v)
(-7(6 + v) + v(6 + v)) = 0
((6 * -7 + v * -7) + v(6 + v)) = 0
((-42 + -7v) + v(6 + v)) = 0
(-42 + -7v + (6 * v + v * v)) = 0
(-42 + -7v + (6v + v2)) = 0

Combine like terms: -7v + 6v = -1v
(-42 + -1v + v2) = 0

Solving
-42 + -1v + v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-6 + -1v)(7 + -1v) = 0

Subproblem 1
Set the factor '(-6 + -1v)' equal to zero and attempt to solve:

Simplifying
-6 + -1v = 0

Solving
-6 + -1v = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1v = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1v = 0 + 6
-1v = 0 + 6

Combine like terms: 0 + 6 = 6
-1v = 6

Divide each side by '-1'.
v = -6

Simplifying
v = -6
Subproblem 2
Set the factor '(7 + -1v)' equal to zero and attempt to solve:

Simplifying
7 + -1v = 0

Solving
7 + -1v = 0

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

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

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

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

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

Simplifying
v = 7
Solution
v = {-6, 7}