(u-3)(u-3)=2u^2-15u+29

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Solution for (u-3)(u-3)=2u^2-15u+29 equation: 


Simplifying
(u + -3)(u + -3) = 2u2 + -15u + 29

Reorder the terms:
(-3 + u)(u + -3) = 2u2 + -15u + 29

Reorder the terms:
(-3 + u)(-3 + u) = 2u2 + -15u + 29

Multiply (-3 + u) * (-3 + u)
(-3(-3 + u) + u(-3 + u)) = 2u2 + -15u + 29
((-3 * -3 + u * -3) + u(-3 + u)) = 2u2 + -15u + 29
((9 + -3u) + u(-3 + u)) = 2u2 + -15u + 29
(9 + -3u + (-3 * u + u * u)) = 2u2 + -15u + 29
(9 + -3u + (-3u + u2)) = 2u2 + -15u + 29

Combine like terms: -3u + -3u = -6u
(9 + -6u + u2) = 2u2 + -15u + 29

Reorder the terms:
9 + -6u + u2 = 29 + -15u + 2u2

Solving
9 + -6u + u2 = 29 + -15u + 2u2

Solving for variable 'u'.

Reorder the terms:
9 + -29 + -6u + 15u + u2 + -2u2 = 29 + -15u + 2u2 + -29 + 15u + -2u2

Combine like terms: 9 + -29 = -20
-20 + -6u + 15u + u2 + -2u2 = 29 + -15u + 2u2 + -29 + 15u + -2u2

Combine like terms: -6u + 15u = 9u
-20 + 9u + u2 + -2u2 = 29 + -15u + 2u2 + -29 + 15u + -2u2

Combine like terms: u2 + -2u2 = -1u2
-20 + 9u + -1u2 = 29 + -15u + 2u2 + -29 + 15u + -2u2

Reorder the terms:
-20 + 9u + -1u2 = 29 + -29 + -15u + 15u + 2u2 + -2u2

Combine like terms: 29 + -29 = 0
-20 + 9u + -1u2 = 0 + -15u + 15u + 2u2 + -2u2
-20 + 9u + -1u2 = -15u + 15u + 2u2 + -2u2

Combine like terms: -15u + 15u = 0
-20 + 9u + -1u2 = 0 + 2u2 + -2u2
-20 + 9u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
-20 + 9u + -1u2 = 0

Factor a trinomial.
(-5 + u)(4 + -1u) = 0


Subproblem 1
Set the factor '(-5 + u)' equal to zero and attempt to solve:

Simplifying
-5 + u = 0

Solving
-5 + u = 0

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

Add '5' to each side of the equation.
-5 + 5 + u = 0 + 5

Combine like terms: -5 + 5 = 0
0 + u = 0 + 5
u = 0 + 5

Combine like terms: 0 + 5 = 5
u = 5

Simplifying
u = 5

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 = {5, 4}

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