2u^2-u-1=(u-1)(u-1)

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Solution for 2u^2-u-1=(u-1)(u-1) equation: 


Simplifying
2u2 + -1u + -1 = (u + -1)(u + -1)

Reorder the terms:
-1 + -1u + 2u2 = (u + -1)(u + -1)

Reorder the terms:
-1 + -1u + 2u2 = (-1 + u)(u + -1)

Reorder the terms:
-1 + -1u + 2u2 = (-1 + u)(-1 + u)

Multiply (-1 + u) * (-1 + u)
-1 + -1u + 2u2 = (-1(-1 + u) + u(-1 + u))
-1 + -1u + 2u2 = ((-1 * -1 + u * -1) + u(-1 + u))
-1 + -1u + 2u2 = ((1 + -1u) + u(-1 + u))
-1 + -1u + 2u2 = (1 + -1u + (-1 * u + u * u))
-1 + -1u + 2u2 = (1 + -1u + (-1u + u2))

Combine like terms: -1u + -1u = -2u
-1 + -1u + 2u2 = (1 + -2u + u2)

Solving
-1 + -1u + 2u2 = 1 + -2u + u2

Solving for variable 'u'.

Reorder the terms:
-1 + -1 + -1u + 2u + 2u2 + -1u2 = 1 + -2u + u2 + -1 + 2u + -1u2

Combine like terms: -1 + -1 = -2
-2 + -1u + 2u + 2u2 + -1u2 = 1 + -2u + u2 + -1 + 2u + -1u2

Combine like terms: -1u + 2u = 1u
-2 + 1u + 2u2 + -1u2 = 1 + -2u + u2 + -1 + 2u + -1u2

Combine like terms: 2u2 + -1u2 = 1u2
-2 + 1u + 1u2 = 1 + -2u + u2 + -1 + 2u + -1u2

Reorder the terms:
-2 + 1u + 1u2 = 1 + -1 + -2u + 2u + u2 + -1u2

Combine like terms: 1 + -1 = 0
-2 + 1u + 1u2 = 0 + -2u + 2u + u2 + -1u2
-2 + 1u + 1u2 = -2u + 2u + u2 + -1u2

Combine like terms: -2u + 2u = 0
-2 + 1u + 1u2 = 0 + u2 + -1u2
-2 + 1u + 1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
-2 + 1u + 1u2 = 0

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


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

Simplifying
-2 + -1u = 0

Solving
-2 + -1u = 0

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

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

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

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

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

Simplifying
u = -2

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

Simplifying
1 + -1u = 0

Solving
1 + -1u = 0

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

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

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

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

Divide each side by '-1'.
u = 1

Simplifying
u = 1
Solution
u = {-2, 1}

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