(v-7)(v+1)=

Solution for (v-7)(v+1)= equation:

Simplifying
(v + -7)(v + 1) = 0

Reorder the terms:
(-7 + v)(v + 1) = 0

Reorder the terms:
(-7 + v)(1 + v) = 0

Multiply (-7 + v) * (1 + v)
(-7(1 + v) + v(1 + v)) = 0
((1 * -7 + v * -7) + v(1 + v)) = 0
((-7 + -7v) + v(1 + v)) = 0
(-7 + -7v + (1 * v + v * v)) = 0
(-7 + -7v + (1v + v2)) = 0

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

Solving
-7 + -6v + v2 = 0

Solving for variable 'v'.

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

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

Simplifying
-1 + -1v = 0

Solving
-1 + -1v = 0

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

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

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

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

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

Simplifying
v = -1
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 = {-1, 7}