(1[2v-9]1)(1[2+v]1)=0

Solution for (1[2v-9]1)(1[2+v]1)=0 equation:

Simplifying
(1[2v + -9] * 1)(1[2 + v] * 1) = 0

Reorder the terms:
(1[-9 + 2v] * 1)(1[2 + v] * 1) = 0

Reorder the terms for easier multiplication:
(1 * 1[-9 + 2v])(1[2 + v] * 1) = 0

Multiply 1 * 1
(1[-9 + 2v])(1[2 + v] * 1) = 0
([-9 * 1 + 2v * 1])(1[2 + v] * 1) = 0
([-9 + 2v])(1[2 + v] * 1) = 0

Reorder the terms for easier multiplication:
(-9 + 2v)(1 * 1[2 + v]) = 0

Multiply 1 * 1
(-9 + 2v)(1[2 + v]) = 0
(-9 + 2v)([2 * 1 + v * 1]) = 0
(-9 + 2v)([2 + 1v]) = 0

Multiply (-9 + 2v) * (2 + 1v)
(-9(2 + 1v) + 2v * (2 + 1v)) = 0
((2 * -9 + 1v * -9) + 2v * (2 + 1v)) = 0
((-18 + -9v) + 2v * (2 + 1v)) = 0
(-18 + -9v + (2 * 2v + 1v * 2v)) = 0
(-18 + -9v + (4v + 2v2)) = 0

Combine like terms: -9v + 4v = -5v
(-18 + -5v + 2v2) = 0

Solving
-18 + -5v + 2v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-2 + -1v)(9 + -2v) = 0

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

Simplifying
-2 + -1v = 0

Solving
-2 + -1v = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1v = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1v = 0 + 2
-1v = 0 + 2

Combine like terms: 0 + 2 = 2
-1v = 2

Divide each side by '-1'.
v = -2

Simplifying
v = -2
Subproblem 2
Set the factor '(9 + -2v)' equal to zero and attempt to solve:

Simplifying
9 + -2v = 0

Solving
9 + -2v = 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 + -2v = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2v = 0 + -9
-2v = 0 + -9

Combine like terms: 0 + -9 = -9
-2v = -9

Divide each side by '-2'.
v = 4.5

Simplifying
v = 4.5
Solution
v = {-2, 4.5}