(u-2)(u-2)=2u^2+u-2

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


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

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

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

Multiply (-2 + u) * (-2 + u)
(-2(-2 + u) + u(-2 + u)) = 2u2 + u + -2
((-2 * -2 + u * -2) + u(-2 + u)) = 2u2 + u + -2
((4 + -2u) + u(-2 + u)) = 2u2 + u + -2
(4 + -2u + (-2 * u + u * u)) = 2u2 + u + -2
(4 + -2u + (-2u + u2)) = 2u2 + u + -2

Combine like terms: -2u + -2u = -4u
(4 + -4u + u2) = 2u2 + u + -2

Reorder the terms:
4 + -4u + u2 = -2 + u + 2u2

Solving
4 + -4u + u2 = -2 + u + 2u2

Solving for variable 'u'.

Reorder the terms:
4 + 2 + -4u + -1u + u2 + -2u2 = -2 + u + 2u2 + 2 + -1u + -2u2

Combine like terms: 4 + 2 = 6
6 + -4u + -1u + u2 + -2u2 = -2 + u + 2u2 + 2 + -1u + -2u2

Combine like terms: -4u + -1u = -5u
6 + -5u + u2 + -2u2 = -2 + u + 2u2 + 2 + -1u + -2u2

Combine like terms: u2 + -2u2 = -1u2
6 + -5u + -1u2 = -2 + u + 2u2 + 2 + -1u + -2u2

Reorder the terms:
6 + -5u + -1u2 = -2 + 2 + u + -1u + 2u2 + -2u2

Combine like terms: -2 + 2 = 0
6 + -5u + -1u2 = 0 + u + -1u + 2u2 + -2u2
6 + -5u + -1u2 = u + -1u + 2u2 + -2u2

Combine like terms: u + -1u = 0
6 + -5u + -1u2 = 0 + 2u2 + -2u2
6 + -5u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
6 + -5u + -1u2 = 0

Factor a trinomial.
(1 + -1u)(6 + u) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(6 + u)' equal to zero and attempt to solve:

Simplifying
6 + u = 0

Solving
6 + u = 0

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

Add '-6' to each side of the equation.
6 + -6 + u = 0 + -6

Combine like terms: 6 + -6 = 0
0 + u = 0 + -6
u = 0 + -6

Combine like terms: 0 + -6 = -6
u = -6

Simplifying
u = -6
Solution
u = {1, -6}

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