2u^2-6u+8=u^2+2u+1

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Solution for 2u^2-6u+8=u^2+2u+1 equation: 


Simplifying
2u2 + -6u + 8 = u2 + 2u + 1

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

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

Solving
8 + -6u + 2u2 = 1 + 2u + u2

Solving for variable 'u'.

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

Combine like terms: 8 + -1 = 7
7 + -6u + -2u + 2u2 + -1u2 = 1 + 2u + u2 + -1 + -2u + -1u2

Combine like terms: -6u + -2u = -8u
7 + -8u + 2u2 + -1u2 = 1 + 2u + u2 + -1 + -2u + -1u2

Combine like terms: 2u2 + -1u2 = 1u2
7 + -8u + 1u2 = 1 + 2u + u2 + -1 + -2u + -1u2

Reorder the terms:
7 + -8u + 1u2 = 1 + -1 + 2u + -2u + u2 + -1u2

Combine like terms: 1 + -1 = 0
7 + -8u + 1u2 = 0 + 2u + -2u + u2 + -1u2
7 + -8u + 1u2 = 2u + -2u + u2 + -1u2

Combine like terms: 2u + -2u = 0
7 + -8u + 1u2 = 0 + u2 + -1u2
7 + -8u + 1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
7 + -8u + 1u2 = 0

Factor a trinomial.
(1 + -1u)(7 + -1u) = 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 '(7 + -1u)' equal to zero and attempt to solve:

Simplifying
7 + -1u = 0

Solving
7 + -1u = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1u = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1u = 0 + -7
-1u = 0 + -7

Combine like terms: 0 + -7 = -7
-1u = -7

Divide each side by '-1'.
u = 7

Simplifying
u = 7
Solution
u = {1, 7}

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