48=(2x-4)(x+3)

Solution for 48=(2x-4)(x+3) equation:

Simplifying
48 = (2x + -4)(x + 3)

Reorder the terms:
48 = (-4 + 2x)(x + 3)

Reorder the terms:
48 = (-4 + 2x)(3 + x)

Multiply (-4 + 2x) * (3 + x)
48 = (-4(3 + x) + 2x * (3 + x))
48 = ((3 * -4 + x * -4) + 2x * (3 + x))
48 = ((-12 + -4x) + 2x * (3 + x))
48 = (-12 + -4x + (3 * 2x + x * 2x))
48 = (-12 + -4x + (6x + 2x2))

Combine like terms: -4x + 6x = 2x
48 = (-12 + 2x + 2x2)

Solving
48 = -12 + 2x + 2x2

Solving for variable 'x'.

Combine like terms: 48 + 12 = 60
60 + -2x + -2x2 = -12 + 2x + 2x2 + 12 + -2x + -2x2

Reorder the terms:
60 + -2x + -2x2 = -12 + 12 + 2x + -2x + 2x2 + -2x2

Combine like terms: -12 + 12 = 0
60 + -2x + -2x2 = 0 + 2x + -2x + 2x2 + -2x2
60 + -2x + -2x2 = 2x + -2x + 2x2 + -2x2

Combine like terms: 2x + -2x = 0
60 + -2x + -2x2 = 0 + 2x2 + -2x2
60 + -2x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
60 + -2x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(30 + -1x + -1x2) = 0

Factor a trinomial.
2((5 + -1x)(6 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {5, -6}