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

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


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

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

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

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

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

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

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

Solving for variable 'v'.

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

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

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

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

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

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

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

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

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

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