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 + -1x2) = 0

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

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

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

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