(u-5)(u-5)=2u^2-15u+29

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Solution for (u-5)(u-5)=2u^2-15u+29 equation: 


Simplifying
(u + -5)(u + -5) = 2u2 + -15u + 29

Reorder the terms:
(-5 + u)(u + -5) = 2u2 + -15u + 29

Reorder the terms:
(-5 + u)(-5 + u) = 2u2 + -15u + 29

Multiply (-5 + u) * (-5 + u)
(-5(-5 + u) + u(-5 + u)) = 2u2 + -15u + 29
((-5 * -5 + u * -5) + u(-5 + u)) = 2u2 + -15u + 29
((25 + -5u) + u(-5 + u)) = 2u2 + -15u + 29
(25 + -5u + (-5 * u + u * u)) = 2u2 + -15u + 29
(25 + -5u + (-5u + u2)) = 2u2 + -15u + 29

Combine like terms: -5u + -5u = -10u
(25 + -10u + u2) = 2u2 + -15u + 29

Reorder the terms:
25 + -10u + u2 = 29 + -15u + 2u2

Solving
25 + -10u + u2 = 29 + -15u + 2u2

Solving for variable 'u'.

Reorder the terms:
25 + -29 + -10u + 15u + u2 + -2u2 = 29 + -15u + 2u2 + -29 + 15u + -2u2

Combine like terms: 25 + -29 = -4
-4 + -10u + 15u + u2 + -2u2 = 29 + -15u + 2u2 + -29 + 15u + -2u2

Combine like terms: -10u + 15u = 5u
-4 + 5u + u2 + -2u2 = 29 + -15u + 2u2 + -29 + 15u + -2u2

Combine like terms: u2 + -2u2 = -1u2
-4 + 5u + -1u2 = 29 + -15u + 2u2 + -29 + 15u + -2u2

Reorder the terms:
-4 + 5u + -1u2 = 29 + -29 + -15u + 15u + 2u2 + -2u2

Combine like terms: 29 + -29 = 0
-4 + 5u + -1u2 = 0 + -15u + 15u + 2u2 + -2u2
-4 + 5u + -1u2 = -15u + 15u + 2u2 + -2u2

Combine like terms: -15u + 15u = 0
-4 + 5u + -1u2 = 0 + 2u2 + -2u2
-4 + 5u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
-4 + 5u + -1u2 = 0

Factor a trinomial.
(-4 + u)(1 + -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 '(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
Solution
u = {4, 1}

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