2(8-x)(x+3)=0

Solution for 2(8-x)(x+3)=0 equation:

Simplifying
2(8 + -1x)(x + 3) = 0

Reorder the terms:
2(8 + -1x)(3 + x) = 0

Multiply (8 + -1x) * (3 + x)
2(8(3 + x) + -1x * (3 + x)) = 0
2((3 * 8 + x * 8) + -1x * (3 + x)) = 0
2((24 + 8x) + -1x * (3 + x)) = 0
2(24 + 8x + (3 * -1x + x * -1x)) = 0
2(24 + 8x + (-3x + -1x2)) = 0

Combine like terms: 8x + -3x = 5x
2(24 + 5x + -1x2) = 0
(24 * 2 + 5x * 2 + -1x2 * 2) = 0
(48 + 10x + -2x2) = 0

Solving
48 + 10x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + 5x + -1x2) = 0

Factor a trinomial.
2((8 + -1x)(3 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {8, -3}