0=-2x^2-8x+24

Solution for 0=-2x^2-8x+24 equation:

Simplifying
0 = -2x2 + -8x + 24

Reorder the terms:
0 = 24 + -8x + -2x2

Solving
0 = 24 + -8x + -2x2

Solving for variable 'x'.

Combine like terms: 0 + -24 = -24
-24 + 8x + 2x2 = 24 + -8x + -2x2 + -24 + 8x + 2x2

Reorder the terms:
-24 + 8x + 2x2 = 24 + -24 + -8x + 8x + -2x2 + 2x2

Combine like terms: 24 + -24 = 0
-24 + 8x + 2x2 = 0 + -8x + 8x + -2x2 + 2x2
-24 + 8x + 2x2 = -8x + 8x + -2x2 + 2x2

Combine like terms: -8x + 8x = 0
-24 + 8x + 2x2 = 0 + -2x2 + 2x2
-24 + 8x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-24 + 8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 4x + x2) = 0

Factor a trinomial.
2((-6 + -1x)(2 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
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 = {-6, 2}