(40-2x)(20-2x)=384

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Solution for (40-2x)(20-2x)=384 equation: 


Simplifying
(40 + -2x)(20 + -2x) = 384

Multiply (40 + -2x) * (20 + -2x)
(40(20 + -2x) + -2x * (20 + -2x)) = 384
((20 * 40 + -2x * 40) + -2x * (20 + -2x)) = 384
((800 + -80x) + -2x * (20 + -2x)) = 384
(800 + -80x + (20 * -2x + -2x * -2x)) = 384
(800 + -80x + (-40x + 4x2)) = 384

Combine like terms: -80x + -40x = -120x
(800 + -120x + 4x2) = 384

Solving
800 + -120x + 4x2 = 384

Solving for variable 'x'.

Reorder the terms:
800 + -384 + -120x + 4x2 = 384 + -384

Combine like terms: 800 + -384 = 416
416 + -120x + 4x2 = 384 + -384

Combine like terms: 384 + -384 = 0
416 + -120x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(104 + -30x + x2) = 0

Factor a trinomial.
4((4 + -1x)(26 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(26 + -1x)' equal to zero and attempt to solve:

Simplifying
26 + -1x = 0

Solving
26 + -1x = 0

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

Add '-26' to each side of the equation.
26 + -26 + -1x = 0 + -26

Combine like terms: 26 + -26 = 0
0 + -1x = 0 + -26
-1x = 0 + -26

Combine like terms: 0 + -26 = -26
-1x = -26

Divide each side by '-1'.
x = 26

Simplifying
x = 26
Solution
x = {4, 26}

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