0=3x^2+6x-24

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Solution for 0=3x^2+6x-24 equation: 


Simplifying
0 = 3x2 + 6x + -24

Reorder the terms:
0 = -24 + 6x + 3x2

Solving
0 = -24 + 6x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 24 = 24
24 + -6x + -3x2 = -24 + 6x + 3x2 + 24 + -6x + -3x2

Reorder the terms:
24 + -6x + -3x2 = -24 + 24 + 6x + -6x + 3x2 + -3x2

Combine like terms: -24 + 24 = 0
24 + -6x + -3x2 = 0 + 6x + -6x + 3x2 + -3x2
24 + -6x + -3x2 = 6x + -6x + 3x2 + -3x2

Combine like terms: 6x + -6x = 0
24 + -6x + -3x2 = 0 + 3x2 + -3x2
24 + -6x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
24 + -6x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + -2x + -1x2) = 0

Factor a trinomial.
3((2 + -1x)(4 + x)) = 0

Ignore the factor 3.

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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {2, -4}

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