u^2-4u-20=3u+24

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Solution for u^2-4u-20=3u+24 equation: 


Simplifying
u2 + -4u + -20 = 3u + 24

Reorder the terms:
-20 + -4u + u2 = 3u + 24

Reorder the terms:
-20 + -4u + u2 = 24 + 3u

Solving
-20 + -4u + u2 = 24 + 3u

Solving for variable 'u'.

Reorder the terms:
-20 + -24 + -4u + -3u + u2 = 24 + 3u + -24 + -3u

Combine like terms: -20 + -24 = -44
-44 + -4u + -3u + u2 = 24 + 3u + -24 + -3u

Combine like terms: -4u + -3u = -7u
-44 + -7u + u2 = 24 + 3u + -24 + -3u

Reorder the terms:
-44 + -7u + u2 = 24 + -24 + 3u + -3u

Combine like terms: 24 + -24 = 0
-44 + -7u + u2 = 0 + 3u + -3u
-44 + -7u + u2 = 3u + -3u

Combine like terms: 3u + -3u = 0
-44 + -7u + u2 = 0

Factor a trinomial.
(-4 + -1u)(11 + -1u) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(11 + -1u)' equal to zero and attempt to solve:

Simplifying
11 + -1u = 0

Solving
11 + -1u = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1u = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1u = 0 + -11
-1u = 0 + -11

Combine like terms: 0 + -11 = -11
-1u = -11

Divide each side by '-1'.
u = 11

Simplifying
u = 11
Solution
u = {-4, 11}

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