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

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

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

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

Multiply (3 + -1x) * (4 + 2x)
(3(4 + 2x) + -1x * (4 + 2x)) = 0
((4 * 3 + 2x * 3) + -1x * (4 + 2x)) = 0
((12 + 6x) + -1x * (4 + 2x)) = 0
(12 + 6x + (4 * -1x + 2x * -1x)) = 0
(12 + 6x + (-4x + -2x2)) = 0

Combine like terms: 6x + -4x = 2x
(12 + 2x + -2x2) = 0

Solving
12 + 2x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + x + -1x2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {3, -2}