(3v+2)-(v+1)=v(2v+3)

Solution for (3v+2)-(v+1)=v(2v+3) equation:

Simplifying
(3v + 2) + -1(v + 1) = v(2v + 3)

Reorder the terms:
(2 + 3v) + -1(v + 1) = v(2v + 3)

Remove parenthesis around (2 + 3v)
2 + 3v + -1(v + 1) = v(2v + 3)

Reorder the terms:
2 + 3v + -1(1 + v) = v(2v + 3)
2 + 3v + (1 * -1 + v * -1) = v(2v + 3)
2 + 3v + (-1 + -1v) = v(2v + 3)

Reorder the terms:
2 + -1 + 3v + -1v = v(2v + 3)

Combine like terms: 2 + -1 = 1
1 + 3v + -1v = v(2v + 3)

Combine like terms: 3v + -1v = 2v
1 + 2v = v(2v + 3)

Reorder the terms:
1 + 2v = v(3 + 2v)
1 + 2v = (3 * v + 2v * v)
1 + 2v = (3v + 2v2)

Solving
1 + 2v = 3v + 2v2

Solving for variable 'v'.

Combine like terms: 2v + -3v = -1v
1 + -1v + -2v2 = 3v + 2v2 + -3v + -2v2

Reorder the terms:
1 + -1v + -2v2 = 3v + -3v + 2v2 + -2v2

Combine like terms: 3v + -3v = 0
1 + -1v + -2v2 = 0 + 2v2 + -2v2
1 + -1v + -2v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
1 + -1v + -2v2 = 0

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

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

Simplifying
1 + -2v = 0

Solving
1 + -2v = 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 + -2v = 0 + -1

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

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

Divide each side by '-2'.
v = 0.5

Simplifying
v = 0.5
Subproblem 2
Set the factor '(1 + v)' equal to zero and attempt to solve:

Simplifying
1 + v = 0

Solving
1 + v = 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 + v = 0 + -1

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

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

Simplifying
v = -1
Solution
v = {0.5, -1}