(x+18)(x+24)=1360

Solution for (x+18)(x+24)=1360 equation:

Simplifying
(x + 18)(x + 24) = 1360

Reorder the terms:
(18 + x)(x + 24) = 1360

Reorder the terms:
(18 + x)(24 + x) = 1360

Multiply (18 + x) * (24 + x)
(18(24 + x) + x(24 + x)) = 1360
((24 * 18 + x * 18) + x(24 + x)) = 1360
((432 + 18x) + x(24 + x)) = 1360
(432 + 18x + (24 * x + x * x)) = 1360
(432 + 18x + (24x + x2)) = 1360

Combine like terms: 18x + 24x = 42x
(432 + 42x + x2) = 1360

Solving
432 + 42x + x2 = 1360

Solving for variable 'x'.

Reorder the terms:
432 + -1360 + 42x + x2 = 1360 + -1360

Combine like terms: 432 + -1360 = -928
-928 + 42x + x2 = 1360 + -1360

Combine like terms: 1360 + -1360 = 0
-928 + 42x + x2 = 0

Factor a trinomial.
(-58 + -1x)(16 + -1x) = 0

Subproblem 1
Set the factor '(-58 + -1x)' equal to zero and attempt to solve:

Simplifying
-58 + -1x = 0

Solving
-58 + -1x = 0

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

Add '58' to each side of the equation.
-58 + 58 + -1x = 0 + 58

Combine like terms: -58 + 58 = 0
0 + -1x = 0 + 58
-1x = 0 + 58

Combine like terms: 0 + 58 = 58
-1x = 58

Divide each side by '-1'.
x = -58

Simplifying
x = -58
Subproblem 2
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {-58, 16}