24=2x^2-4x-24

Solution for 24=2x^2-4x-24 equation:

Simplifying
24 = 2x2 + -4x + -24

Reorder the terms:
24 = -24 + -4x + 2x2

Solving
24 = -24 + -4x + 2x2

Solving for variable 'x'.

Combine like terms: 24 + 24 = 48
48 + 4x + -2x2 = -24 + -4x + 2x2 + 24 + 4x + -2x2

Reorder the terms:
48 + 4x + -2x2 = -24 + 24 + -4x + 4x + 2x2 + -2x2

Combine like terms: -24 + 24 = 0
48 + 4x + -2x2 = 0 + -4x + 4x + 2x2 + -2x2
48 + 4x + -2x2 = -4x + 4x + 2x2 + -2x2

Combine like terms: -4x + 4x = 0
48 + 4x + -2x2 = 0 + 2x2 + -2x2
48 + 4x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
48 + 4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + 2x + -1x2) = 0

Factor a trinomial.
2((6 + -1x)(4 + x)) = 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 '(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 = {6, -4}