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

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


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

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

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

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

Multiply (-1 + v) * (-1 + v)
-1 + -3v + 2v2 = (-1(-1 + v) + v(-1 + v))
-1 + -3v + 2v2 = ((-1 * -1 + v * -1) + v(-1 + v))
-1 + -3v + 2v2 = ((1 + -1v) + v(-1 + v))
-1 + -3v + 2v2 = (1 + -1v + (-1 * v + v * v))
-1 + -3v + 2v2 = (1 + -1v + (-1v + v2))

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

Solving
-1 + -3v + 2v2 = 1 + -2v + v2

Solving for variable 'v'.

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

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

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

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

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

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

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

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

Factor a trinomial.
(-1 + -1v)(2 + -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 '(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
Solution
v = {-1, 2}

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