2(x+3)(4-x)=0

Solution for 2(x+3)(4-x)=0 equation:

Simplifying
2(x + 3)(4 + -1x) = 0

Reorder the terms:
2(3 + x)(4 + -1x) = 0

Multiply (3 + x) * (4 + -1x)
2(3(4 + -1x) + x(4 + -1x)) = 0
2((4 * 3 + -1x * 3) + x(4 + -1x)) = 0
2((12 + -3x) + x(4 + -1x)) = 0
2(12 + -3x + (4 * x + -1x * x)) = 0
2(12 + -3x + (4x + -1x2)) = 0

Combine like terms: -3x + 4x = 1x
2(12 + 1x + -1x2) = 0
(12 * 2 + 1x * 2 + -1x2 * 2) = 0
(24 + 2x + -2x2) = 0

Solving
24 + 2x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + x + -1x2) = 0

Factor a trinomial.
2((4 + -1x)(3 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
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 = {4, -3}