x(8+x)=4080

Solution for x(8+x)=4080 equation:

Simplifying
x(8 + x) = 4080
(8 * x + x * x) = 4080
(8x + x2) = 4080

Solving
8x + x2 = 4080

Solving for variable 'x'.

Reorder the terms:
-4080 + 8x + x2 = 4080 + -4080

Combine like terms: 4080 + -4080 = 0
-4080 + 8x + x2 = 0

Factor a trinomial.
(-68 + -1x)(60 + -1x) = 0

Subproblem 1
Set the factor '(-68 + -1x)' equal to zero and attempt to solve:

Simplifying
-68 + -1x = 0

Solving
-68 + -1x = 0

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

Add '68' to each side of the equation.
-68 + 68 + -1x = 0 + 68

Combine like terms: -68 + 68 = 0
0 + -1x = 0 + 68
-1x = 0 + 68

Combine like terms: 0 + 68 = 68
-1x = 68

Divide each side by '-1'.
x = -68

Simplifying
x = -68
Subproblem 2
Set the factor '(60 + -1x)' equal to zero and attempt to solve:

Simplifying
60 + -1x = 0

Solving
60 + -1x = 0

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

Add '-60' to each side of the equation.
60 + -60 + -1x = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -1x = 0 + -60
-1x = 0 + -60

Combine like terms: 0 + -60 = -60
-1x = -60

Divide each side by '-1'.
x = 60

Simplifying
x = 60
Solution
x = {-68, 60}