(30-2x)(20-2x)=200

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Solution for (30-2x)(20-2x)=200 equation: 


Simplifying
(30 + -2x)(20 + -2x) = 200

Multiply (30 + -2x) * (20 + -2x)
(30(20 + -2x) + -2x * (20 + -2x)) = 200
((20 * 30 + -2x * 30) + -2x * (20 + -2x)) = 200
((600 + -60x) + -2x * (20 + -2x)) = 200
(600 + -60x + (20 * -2x + -2x * -2x)) = 200
(600 + -60x + (-40x + 4x2)) = 200

Combine like terms: -60x + -40x = -100x
(600 + -100x + 4x2) = 200

Solving
600 + -100x + 4x2 = 200

Solving for variable 'x'.

Reorder the terms:
600 + -200 + -100x + 4x2 = 200 + -200

Combine like terms: 600 + -200 = 400
400 + -100x + 4x2 = 200 + -200

Combine like terms: 200 + -200 = 0
400 + -100x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(100 + -25x + x2) = 0

Factor a trinomial.
4((5 + -1x)(20 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Solution
x = {5, 20}

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