(v+3)(v-3)=8v

Solution for (v+3)(v-3)=8v equation:

Simplifying
(v + 3)(v + -3) = 8v

Reorder the terms:
(3 + v)(v + -3) = 8v

Reorder the terms:
(3 + v)(-3 + v) = 8v

Multiply (3 + v) * (-3 + v)
(3(-3 + v) + v(-3 + v)) = 8v
((-3 * 3 + v * 3) + v(-3 + v)) = 8v
((-9 + 3v) + v(-3 + v)) = 8v
(-9 + 3v + (-3 * v + v * v)) = 8v
(-9 + 3v + (-3v + v2)) = 8v

Combine like terms: 3v + -3v = 0
(-9 + 0 + v2) = 8v
(-9 + v2) = 8v

Solving
-9 + v2 = 8v

Solving for variable 'v'.

Reorder the terms:
-9 + -8v + v2 = 8v + -8v

Combine like terms: 8v + -8v = 0
-9 + -8v + v2 = 0

Factor a trinomial.
(-1 + -1v)(9 + -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 '(9 + -1v)' equal to zero and attempt to solve:

Simplifying
9 + -1v = 0

Solving
9 + -1v = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1v = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1v = 0 + -9
-1v = 0 + -9

Combine like terms: 0 + -9 = -9
-1v = -9

Divide each side by '-1'.
v = 9

Simplifying
v = 9
Solution
v = {-1, 9}