0=24-5x-x^2

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Solution for 0=24-5x-x^2 equation: 


Simplifying
0 = 24 + -5x + -1x2

Solving
0 = 24 + -5x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + -24 = -24
-24 + 5x + x2 = 24 + -5x + -1x2 + -24 + 5x + x2

Reorder the terms:
-24 + 5x + x2 = 24 + -24 + -5x + 5x + -1x2 + x2

Combine like terms: 24 + -24 = 0
-24 + 5x + x2 = 0 + -5x + 5x + -1x2 + x2
-24 + 5x + x2 = -5x + 5x + -1x2 + x2

Combine like terms: -5x + 5x = 0
-24 + 5x + x2 = 0 + -1x2 + x2
-24 + 5x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-24 + 5x + x2 = 0

Factor a trinomial.
(-8 + -1x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

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

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

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

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

Simplifying
x = 3
Solution
x = {-8, 3}

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