(u-5)(u-5)=2u^2-14u+20

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Solution for (u-5)(u-5)=2u^2-14u+20 equation: 


Simplifying
(u + -5)(u + -5) = 2u2 + -14u + 20

Reorder the terms:
(-5 + u)(u + -5) = 2u2 + -14u + 20

Reorder the terms:
(-5 + u)(-5 + u) = 2u2 + -14u + 20

Multiply (-5 + u) * (-5 + u)
(-5(-5 + u) + u(-5 + u)) = 2u2 + -14u + 20
((-5 * -5 + u * -5) + u(-5 + u)) = 2u2 + -14u + 20
((25 + -5u) + u(-5 + u)) = 2u2 + -14u + 20
(25 + -5u + (-5 * u + u * u)) = 2u2 + -14u + 20
(25 + -5u + (-5u + u2)) = 2u2 + -14u + 20

Combine like terms: -5u + -5u = -10u
(25 + -10u + u2) = 2u2 + -14u + 20

Reorder the terms:
25 + -10u + u2 = 20 + -14u + 2u2

Solving
25 + -10u + u2 = 20 + -14u + 2u2

Solving for variable 'u'.

Reorder the terms:
25 + -20 + -10u + 14u + u2 + -2u2 = 20 + -14u + 2u2 + -20 + 14u + -2u2

Combine like terms: 25 + -20 = 5
5 + -10u + 14u + u2 + -2u2 = 20 + -14u + 2u2 + -20 + 14u + -2u2

Combine like terms: -10u + 14u = 4u
5 + 4u + u2 + -2u2 = 20 + -14u + 2u2 + -20 + 14u + -2u2

Combine like terms: u2 + -2u2 = -1u2
5 + 4u + -1u2 = 20 + -14u + 2u2 + -20 + 14u + -2u2

Reorder the terms:
5 + 4u + -1u2 = 20 + -20 + -14u + 14u + 2u2 + -2u2

Combine like terms: 20 + -20 = 0
5 + 4u + -1u2 = 0 + -14u + 14u + 2u2 + -2u2
5 + 4u + -1u2 = -14u + 14u + 2u2 + -2u2

Combine like terms: -14u + 14u = 0
5 + 4u + -1u2 = 0 + 2u2 + -2u2
5 + 4u + -1u2 = 2u2 + -2u2

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

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


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

Simplifying
5 + -1u = 0

Solving
5 + -1u = 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 + -1u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1u = 0 + -5
-1u = 0 + -5

Combine like terms: 0 + -5 = -5
-1u = -5

Divide each side by '-1'.
u = 5

Simplifying
u = 5

Subproblem 2
Set the factor '(1 + u)' equal to zero and attempt to solve:

Simplifying
1 + u = 0

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

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

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

Simplifying
u = -1
Solution
u = {5, -1}

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