48=(x+2)(x)2

Solution for 48=(x+2)(x)2 equation:

Simplifying
48 = (x + 2)(x) * 2

Reorder the terms:
48 = (2 + x)(x) * 2

Reorder the terms for easier multiplication:
48 = 2x(2 + x)
48 = (2 * 2x + x * 2x)
48 = (4x + 2x2)

Solving
48 = 4x + 2x2

Solving for variable 'x'.

Reorder the terms:
48 + -4x + -2x2 = 4x + -4x + 2x2 + -2x2

Combine like terms: 4x + -4x = 0
48 + -4x + -2x2 = 0 + 2x2 + -2x2
48 + -4x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
48 + -4x + -2x2 = 0

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

Factor a trinomial.
2((4 + -1x)(6 + 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 '(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 = {4, -6}