0=(x*x)+(10*x)-24

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Solution for 0=(x*x)+(10*x)-24 equation: 


Simplifying
0 = (x * x) + (10x) + -24

Multiply x * x
0 = (x2) + (10x) + -24
0 = x2 + (10x) + -24

Reorder the terms:
0 = -24 + (10x) + x2

Solving
0 = -24 + (10x) + x2

Solving for variable 'x'.

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

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

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

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

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

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


Subproblem 1
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

Subproblem 2
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 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 + x = 0 + -12

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

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

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

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