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

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


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

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

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

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

Solving for variable 'u'.

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

Combine like terms: -16 + -4 = -20
-20 + 5u + -4u + 2u2 + -1u2 = 4 + 4u + u2 + -4 + -4u + -1u2

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

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

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

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

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

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

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