384=x(20+x)

Solution for 384=x(20+x) equation:

Simplifying
384 = x(20 + x)
384 = (20 * x + x * x)
384 = (20x + x2)

Solving
384 = 20x + x2

Solving for variable 'x'.

Reorder the terms:
384 + -20x + -1x2 = 20x + -20x + x2 + -1x2

Combine like terms: 20x + -20x = 0
384 + -20x + -1x2 = 0 + x2 + -1x2
384 + -20x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
384 + -20x + -1x2 = 0

Factor a trinomial.
(12 + -1x)(32 + x) = 0

Subproblem 1
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Subproblem 2
Set the factor '(32 + x)' equal to zero and attempt to solve:

Simplifying
32 + x = 0

Solving
32 + x = 0

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

Add '-32' to each side of the equation.
32 + -32 + x = 0 + -32

Combine like terms: 32 + -32 = 0
0 + x = 0 + -32
x = 0 + -32

Combine like terms: 0 + -32 = -32
x = -32

Simplifying
x = -32
Solution
x = {12, -32}