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

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

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

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

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

Multiply (2 + x) * (-4 + x)
48 = 3(2(-4 + x) + x(-4 + x))
48 = 3((-4 * 2 + x * 2) + x(-4 + x))
48 = 3((-8 + 2x) + x(-4 + x))
48 = 3(-8 + 2x + (-4 * x + x * x))
48 = 3(-8 + 2x + (-4x + x2))

Combine like terms: 2x + -4x = -2x
48 = 3(-8 + -2x + x2)
48 = (-8 * 3 + -2x * 3 + x2 * 3)
48 = (-24 + -6x + 3x2)

Solving
48 = -24 + -6x + 3x2

Solving for variable 'x'.

Combine like terms: 48 + 24 = 72
72 + 6x + -3x2 = -24 + -6x + 3x2 + 24 + 6x + -3x2

Reorder the terms:
72 + 6x + -3x2 = -24 + 24 + -6x + 6x + 3x2 + -3x2

Combine like terms: -24 + 24 = 0
72 + 6x + -3x2 = 0 + -6x + 6x + 3x2 + -3x2
72 + 6x + -3x2 = -6x + 6x + 3x2 + -3x2

Combine like terms: -6x + 6x = 0
72 + 6x + -3x2 = 0 + 3x2 + -3x2
72 + 6x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
72 + 6x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(24 + 2x + -1x2) = 0

Factor a trinomial.
3((6 + -1x)(4 + x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

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

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

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

Simplifying
x = -4
Solution
x = {6, -4}