2u^2-8u+1=(u-5)(u-5)

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Solution for 2u^2-8u+1=(u-5)(u-5) equation: 


Simplifying
2u2 + -8u + 1 = (u + -5)(u + -5)

Reorder the terms:
1 + -8u + 2u2 = (u + -5)(u + -5)

Reorder the terms:
1 + -8u + 2u2 = (-5 + u)(u + -5)

Reorder the terms:
1 + -8u + 2u2 = (-5 + u)(-5 + u)

Multiply (-5 + u) * (-5 + u)
1 + -8u + 2u2 = (-5(-5 + u) + u(-5 + u))
1 + -8u + 2u2 = ((-5 * -5 + u * -5) + u(-5 + u))
1 + -8u + 2u2 = ((25 + -5u) + u(-5 + u))
1 + -8u + 2u2 = (25 + -5u + (-5 * u + u * u))
1 + -8u + 2u2 = (25 + -5u + (-5u + u2))

Combine like terms: -5u + -5u = -10u
1 + -8u + 2u2 = (25 + -10u + u2)

Solving
1 + -8u + 2u2 = 25 + -10u + u2

Solving for variable 'u'.

Reorder the terms:
1 + -25 + -8u + 10u + 2u2 + -1u2 = 25 + -10u + u2 + -25 + 10u + -1u2

Combine like terms: 1 + -25 = -24
-24 + -8u + 10u + 2u2 + -1u2 = 25 + -10u + u2 + -25 + 10u + -1u2

Combine like terms: -8u + 10u = 2u
-24 + 2u + 2u2 + -1u2 = 25 + -10u + u2 + -25 + 10u + -1u2

Combine like terms: 2u2 + -1u2 = 1u2
-24 + 2u + 1u2 = 25 + -10u + u2 + -25 + 10u + -1u2

Reorder the terms:
-24 + 2u + 1u2 = 25 + -25 + -10u + 10u + u2 + -1u2

Combine like terms: 25 + -25 = 0
-24 + 2u + 1u2 = 0 + -10u + 10u + u2 + -1u2
-24 + 2u + 1u2 = -10u + 10u + u2 + -1u2

Combine like terms: -10u + 10u = 0
-24 + 2u + 1u2 = 0 + u2 + -1u2
-24 + 2u + 1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
-24 + 2u + 1u2 = 0

Factor a trinomial.
(-6 + -1u)(4 + -1u) = 0


Subproblem 1
Set the factor '(-6 + -1u)' equal to zero and attempt to solve:

Simplifying
-6 + -1u = 0

Solving
-6 + -1u = 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 + -1u = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1u = 0 + 6
-1u = 0 + 6

Combine like terms: 0 + 6 = 6
-1u = 6

Divide each side by '-1'.
u = -6

Simplifying
u = -6

Subproblem 2
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
Solution
u = {-6, 4}

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