0=24-10x-x^2

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Solution for 0=24-10x-x^2 equation: 


Simplifying
0 = 24 + -10x + -1x2

Solving
0 = 24 + -10x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + -24 = -24
-24 + 10x + x2 = 24 + -10x + -1x2 + -24 + 10x + x2

Reorder the terms:
-24 + 10x + x2 = 24 + -24 + -10x + 10x + -1x2 + x2

Combine like terms: 24 + -24 = 0
-24 + 10x + x2 = 0 + -10x + 10x + -1x2 + x2
-24 + 10x + x2 = -10x + 10x + -1x2 + x2

Combine like terms: -10x + 10x = 0
-24 + 10x + x2 = 0 + -1x2 + x2
-24 + 10x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-24 + 10x + x2 = 0

Factor a trinomial.
(-12 + -1x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-12, 2}

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