2u^2-4u+1=(u-3)(u-3)

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Solution for 2u^2-4u+1=(u-3)(u-3) equation: 


Simplifying
2u2 + -4u + 1 = (u + -3)(u + -3)

Reorder the terms:
1 + -4u + 2u2 = (u + -3)(u + -3)

Reorder the terms:
1 + -4u + 2u2 = (-3 + u)(u + -3)

Reorder the terms:
1 + -4u + 2u2 = (-3 + u)(-3 + u)

Multiply (-3 + u) * (-3 + u)
1 + -4u + 2u2 = (-3(-3 + u) + u(-3 + u))
1 + -4u + 2u2 = ((-3 * -3 + u * -3) + u(-3 + u))
1 + -4u + 2u2 = ((9 + -3u) + u(-3 + u))
1 + -4u + 2u2 = (9 + -3u + (-3 * u + u * u))
1 + -4u + 2u2 = (9 + -3u + (-3u + u2))

Combine like terms: -3u + -3u = -6u
1 + -4u + 2u2 = (9 + -6u + u2)

Solving
1 + -4u + 2u2 = 9 + -6u + u2

Solving for variable 'u'.

Reorder the terms:
1 + -9 + -4u + 6u + 2u2 + -1u2 = 9 + -6u + u2 + -9 + 6u + -1u2

Combine like terms: 1 + -9 = -8
-8 + -4u + 6u + 2u2 + -1u2 = 9 + -6u + u2 + -9 + 6u + -1u2

Combine like terms: -4u + 6u = 2u
-8 + 2u + 2u2 + -1u2 = 9 + -6u + u2 + -9 + 6u + -1u2

Combine like terms: 2u2 + -1u2 = 1u2
-8 + 2u + 1u2 = 9 + -6u + u2 + -9 + 6u + -1u2

Reorder the terms:
-8 + 2u + 1u2 = 9 + -9 + -6u + 6u + u2 + -1u2

Combine like terms: 9 + -9 = 0
-8 + 2u + 1u2 = 0 + -6u + 6u + u2 + -1u2
-8 + 2u + 1u2 = -6u + 6u + u2 + -1u2

Combine like terms: -6u + 6u = 0
-8 + 2u + 1u2 = 0 + u2 + -1u2
-8 + 2u + 1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
-8 + 2u + 1u2 = 0

Factor a trinomial.
(-4 + -1u)(2 + -1u) = 0


Subproblem 1
Set the factor '(-4 + -1u)' equal to zero and attempt to solve:

Simplifying
-4 + -1u = 0

Solving
-4 + -1u = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1u = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1u = 0 + 4
-1u = 0 + 4

Combine like terms: 0 + 4 = 4
-1u = 4

Divide each side by '-1'.
u = -4

Simplifying
u = -4

Subproblem 2
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
Solution
u = {-4, 2}

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