(20+2x)(22+2x)=728

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Solution for (20+2x)(22+2x)=728 equation: 


Simplifying
(20 + 2x)(22 + 2x) = 728

Multiply (20 + 2x) * (22 + 2x)
(20(22 + 2x) + 2x * (22 + 2x)) = 728
((22 * 20 + 2x * 20) + 2x * (22 + 2x)) = 728
((440 + 40x) + 2x * (22 + 2x)) = 728
(440 + 40x + (22 * 2x + 2x * 2x)) = 728
(440 + 40x + (44x + 4x2)) = 728

Combine like terms: 40x + 44x = 84x
(440 + 84x + 4x2) = 728

Solving
440 + 84x + 4x2 = 728

Solving for variable 'x'.

Reorder the terms:
440 + -728 + 84x + 4x2 = 728 + -728

Combine like terms: 440 + -728 = -288
-288 + 84x + 4x2 = 728 + -728

Combine like terms: 728 + -728 = 0
-288 + 84x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-72 + 21x + x2) = 0

Factor a trinomial.
4((-24 + -1x)(3 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-24 + -1x)' equal to zero and attempt to solve:

Simplifying
-24 + -1x = 0

Solving
-24 + -1x = 0

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

Add '24' to each side of the equation.
-24 + 24 + -1x = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -1x = 0 + 24
-1x = 0 + 24

Combine like terms: 0 + 24 = 24
-1x = 24

Divide each side by '-1'.
x = -24

Simplifying
x = -24

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-24, 3}

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