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 + x2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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 = {-4, 2}

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