(u-3)(u-3)=2u^2-12u+17

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Solution for (u-3)(u-3)=2u^2-12u+17 equation: 


Simplifying
(u + -3)(u + -3) = 2u2 + -12u + 17

Reorder the terms:
(-3 + u)(u + -3) = 2u2 + -12u + 17

Reorder the terms:
(-3 + u)(-3 + u) = 2u2 + -12u + 17

Multiply (-3 + u) * (-3 + u)
(-3(-3 + u) + u(-3 + u)) = 2u2 + -12u + 17
((-3 * -3 + u * -3) + u(-3 + u)) = 2u2 + -12u + 17
((9 + -3u) + u(-3 + u)) = 2u2 + -12u + 17
(9 + -3u + (-3 * u + u * u)) = 2u2 + -12u + 17
(9 + -3u + (-3u + u2)) = 2u2 + -12u + 17

Combine like terms: -3u + -3u = -6u
(9 + -6u + u2) = 2u2 + -12u + 17

Reorder the terms:
9 + -6u + u2 = 17 + -12u + 2u2

Solving
9 + -6u + u2 = 17 + -12u + 2u2

Solving for variable 'u'.

Reorder the terms:
9 + -17 + -6u + 12u + u2 + -2u2 = 17 + -12u + 2u2 + -17 + 12u + -2u2

Combine like terms: 9 + -17 = -8
-8 + -6u + 12u + u2 + -2u2 = 17 + -12u + 2u2 + -17 + 12u + -2u2

Combine like terms: -6u + 12u = 6u
-8 + 6u + u2 + -2u2 = 17 + -12u + 2u2 + -17 + 12u + -2u2

Combine like terms: u2 + -2u2 = -1u2
-8 + 6u + -1u2 = 17 + -12u + 2u2 + -17 + 12u + -2u2

Reorder the terms:
-8 + 6u + -1u2 = 17 + -17 + -12u + 12u + 2u2 + -2u2

Combine like terms: 17 + -17 = 0
-8 + 6u + -1u2 = 0 + -12u + 12u + 2u2 + -2u2
-8 + 6u + -1u2 = -12u + 12u + 2u2 + -2u2

Combine like terms: -12u + 12u = 0
-8 + 6u + -1u2 = 0 + 2u2 + -2u2
-8 + 6u + -1u2 = 2u2 + -2u2

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

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


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

Simplifying
-4 + u = 0

Solving
-4 + u = 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 + u = 0 + 4

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

Combine like terms: 0 + 4 = 4
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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