(18+2x)(24+2x)=1360

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Solution for (18+2x)(24+2x)=1360 equation: 


Simplifying
(18 + 2x)(24 + 2x) = 1360

Multiply (18 + 2x) * (24 + 2x)
(18(24 + 2x) + 2x * (24 + 2x)) = 1360
((24 * 18 + 2x * 18) + 2x * (24 + 2x)) = 1360
((432 + 36x) + 2x * (24 + 2x)) = 1360
(432 + 36x + (24 * 2x + 2x * 2x)) = 1360
(432 + 36x + (48x + 4x2)) = 1360

Combine like terms: 36x + 48x = 84x
(432 + 84x + 4x2) = 1360

Solving
432 + 84x + 4x2 = 1360

Solving for variable 'x'.

Reorder the terms:
432 + -1360 + 84x + 4x2 = 1360 + -1360

Combine like terms: 432 + -1360 = -928
-928 + 84x + 4x2 = 1360 + -1360

Combine like terms: 1360 + -1360 = 0
-928 + 84x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-232 + 21x + x2) = 0

Factor a trinomial.
4((-29 + -1x)(8 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-29 + -1x)' equal to zero and attempt to solve:

Simplifying
-29 + -1x = 0

Solving
-29 + -1x = 0

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

Add '29' to each side of the equation.
-29 + 29 + -1x = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -1x = 0 + 29
-1x = 0 + 29

Combine like terms: 0 + 29 = 29
-1x = 29

Divide each side by '-1'.
x = -29

Simplifying
x = -29

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-29, 8}

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