2u^2-4u-5=u^2-8u+16

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Solution for 2u^2-4u-5=u^2-8u+16 equation: 


Simplifying
2u2 + -4u + -5 = u2 + -8u + 16

Reorder the terms:
-5 + -4u + 2u2 = u2 + -8u + 16

Reorder the terms:
-5 + -4u + 2u2 = 16 + -8u + u2

Solving
-5 + -4u + 2u2 = 16 + -8u + u2

Solving for variable 'u'.

Reorder the terms:
-5 + -16 + -4u + 8u + 2u2 + -1u2 = 16 + -8u + u2 + -16 + 8u + -1u2

Combine like terms: -5 + -16 = -21
-21 + -4u + 8u + 2u2 + -1u2 = 16 + -8u + u2 + -16 + 8u + -1u2

Combine like terms: -4u + 8u = 4u
-21 + 4u + 2u2 + -1u2 = 16 + -8u + u2 + -16 + 8u + -1u2

Combine like terms: 2u2 + -1u2 = 1u2
-21 + 4u + 1u2 = 16 + -8u + u2 + -16 + 8u + -1u2

Reorder the terms:
-21 + 4u + 1u2 = 16 + -16 + -8u + 8u + u2 + -1u2

Combine like terms: 16 + -16 = 0
-21 + 4u + 1u2 = 0 + -8u + 8u + u2 + -1u2
-21 + 4u + 1u2 = -8u + 8u + u2 + -1u2

Combine like terms: -8u + 8u = 0
-21 + 4u + 1u2 = 0 + u2 + -1u2
-21 + 4u + 1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
-21 + 4u + 1u2 = 0

Factor a trinomial.
(-7 + -1u)(3 + -1u) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(3 + -1u)' equal to zero and attempt to solve:

Simplifying
3 + -1u = 0

Solving
3 + -1u = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1u = 0 + -3
-1u = 0 + -3

Combine like terms: 0 + -3 = -3
-1u = -3

Divide each side by '-1'.
u = 3

Simplifying
u = 3
Solution
u = {-7, 3}

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