(3v-2)(2v+1)=3v^2-11v-10

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Solution for (3v-2)(2v+1)=3v^2-11v-10 equation: 


Simplifying
(3v + -2)(2v + 1) = 3v2 + -11v + -10

Reorder the terms:
(-2 + 3v)(2v + 1) = 3v2 + -11v + -10

Reorder the terms:
(-2 + 3v)(1 + 2v) = 3v2 + -11v + -10

Multiply (-2 + 3v) * (1 + 2v)
(-2(1 + 2v) + 3v * (1 + 2v)) = 3v2 + -11v + -10
((1 * -2 + 2v * -2) + 3v * (1 + 2v)) = 3v2 + -11v + -10
((-2 + -4v) + 3v * (1 + 2v)) = 3v2 + -11v + -10
(-2 + -4v + (1 * 3v + 2v * 3v)) = 3v2 + -11v + -10
(-2 + -4v + (3v + 6v2)) = 3v2 + -11v + -10

Combine like terms: -4v + 3v = -1v
(-2 + -1v + 6v2) = 3v2 + -11v + -10

Reorder the terms:
-2 + -1v + 6v2 = -10 + -11v + 3v2

Solving
-2 + -1v + 6v2 = -10 + -11v + 3v2

Solving for variable 'v'.

Reorder the terms:
-2 + 10 + -1v + 11v + 6v2 + -3v2 = -10 + -11v + 3v2 + 10 + 11v + -3v2

Combine like terms: -2 + 10 = 8
8 + -1v + 11v + 6v2 + -3v2 = -10 + -11v + 3v2 + 10 + 11v + -3v2

Combine like terms: -1v + 11v = 10v
8 + 10v + 6v2 + -3v2 = -10 + -11v + 3v2 + 10 + 11v + -3v2

Combine like terms: 6v2 + -3v2 = 3v2
8 + 10v + 3v2 = -10 + -11v + 3v2 + 10 + 11v + -3v2

Reorder the terms:
8 + 10v + 3v2 = -10 + 10 + -11v + 11v + 3v2 + -3v2

Combine like terms: -10 + 10 = 0
8 + 10v + 3v2 = 0 + -11v + 11v + 3v2 + -3v2
8 + 10v + 3v2 = -11v + 11v + 3v2 + -3v2

Combine like terms: -11v + 11v = 0
8 + 10v + 3v2 = 0 + 3v2 + -3v2
8 + 10v + 3v2 = 3v2 + -3v2

Combine like terms: 3v2 + -3v2 = 0
8 + 10v + 3v2 = 0

Factor a trinomial.
(2 + v)(4 + 3v) = 0


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

Simplifying
2 + v = 0

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

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

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

Simplifying
v = -2

Subproblem 2
Set the factor '(4 + 3v)' equal to zero and attempt to solve:

Simplifying
4 + 3v = 0

Solving
4 + 3v = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3v = 0 + -4
3v = 0 + -4

Combine like terms: 0 + -4 = -4
3v = -4

Divide each side by '3'.
v = -1.333333333

Simplifying
v = -1.333333333
Solution
v = {-2, -1.333333333}

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