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

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

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

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

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

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

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

Solving
0 = -12 + 2x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 12 = 12
12 + -2x + -2x2 = -12 + 2x + 2x2 + 12 + -2x + -2x2

Reorder the terms:
12 + -2x + -2x2 = -12 + 12 + 2x + -2x + 2x2 + -2x2

Combine like terms: -12 + 12 = 0
12 + -2x + -2x2 = 0 + 2x + -2x + 2x2 + -2x2
12 + -2x + -2x2 = 2x + -2x + 2x2 + -2x2

Combine like terms: 2x + -2x = 0
12 + -2x + -2x2 = 0 + 2x2 + -2x2
12 + -2x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
12 + -2x + -2x2 = 0

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

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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
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 = {2, -3}