(x+24)(x+10)=480

Solution for (x+24)(x+10)=480 equation:

Simplifying
(x + 24)(x + 10) = 480

Reorder the terms:
(24 + x)(x + 10) = 480

Reorder the terms:
(24 + x)(10 + x) = 480

Multiply (24 + x) * (10 + x)
(24(10 + x) + x(10 + x)) = 480
((10 * 24 + x * 24) + x(10 + x)) = 480
((240 + 24x) + x(10 + x)) = 480
(240 + 24x + (10 * x + x * x)) = 480
(240 + 24x + (10x + x2)) = 480

Combine like terms: 24x + 10x = 34x
(240 + 34x + x2) = 480

Solving
240 + 34x + x2 = 480

Solving for variable 'x'.

Reorder the terms:
240 + -480 + 34x + x2 = 480 + -480

Combine like terms: 240 + -480 = -240
-240 + 34x + x2 = 480 + -480

Combine like terms: 480 + -480 = 0
-240 + 34x + x2 = 0

Factor a trinomial.
(-40 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-40 + -1x)' equal to zero and attempt to solve:

Simplifying
-40 + -1x = 0

Solving
-40 + -1x = 0

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

Add '40' to each side of the equation.
-40 + 40 + -1x = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -1x = 0 + 40
-1x = 0 + 40

Combine like terms: 0 + 40 = 40
-1x = 40

Divide each side by '-1'.
x = -40

Simplifying
x = -40
Subproblem 2
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
Solution
x = {-40, 6}