-2(x^2+8x-768)=0

Solution for -2(x^2+8x-768)=0 equation:

Simplifying
-2(x2 + 8x + -768) = 0

Reorder the terms:
-2(-768 + 8x + x2) = 0
(-768 * -2 + 8x * -2 + x2 * -2) = 0
(1536 + -16x + -2x2) = 0

Solving
1536 + -16x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(768 + -8x + -1x2) = 0

Factor a trinomial.
2((24 + -1x)(32 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(24 + -1x)' equal to zero and attempt to solve:

Simplifying
24 + -1x = 0

Solving
24 + -1x = 0

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

Add '-24' to each side of the equation.
24 + -24 + -1x = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -1x = 0 + -24
-1x = 0 + -24

Combine like terms: 0 + -24 = -24
-1x = -24

Divide each side by '-1'.
x = 24

Simplifying
x = 24
Subproblem 2
Set the factor '(32 + x)' equal to zero and attempt to solve:

Simplifying
32 + x = 0

Solving
32 + x = 0

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

Add '-32' to each side of the equation.
32 + -32 + x = 0 + -32

Combine like terms: 32 + -32 = 0
0 + x = 0 + -32
x = 0 + -32

Combine like terms: 0 + -32 = -32
x = -32

Simplifying
x = -32
Solution
x = {24, -32}