(18-2x)(20-2x)=224

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Solution for (18-2x)(20-2x)=224 equation: 


Simplifying
(18 + -2x)(20 + -2x) = 224

Multiply (18 + -2x) * (20 + -2x)
(18(20 + -2x) + -2x * (20 + -2x)) = 224
((20 * 18 + -2x * 18) + -2x * (20 + -2x)) = 224
((360 + -36x) + -2x * (20 + -2x)) = 224
(360 + -36x + (20 * -2x + -2x * -2x)) = 224
(360 + -36x + (-40x + 4x2)) = 224

Combine like terms: -36x + -40x = -76x
(360 + -76x + 4x2) = 224

Solving
360 + -76x + 4x2 = 224

Solving for variable 'x'.

Reorder the terms:
360 + -224 + -76x + 4x2 = 224 + -224

Combine like terms: 360 + -224 = 136
136 + -76x + 4x2 = 224 + -224

Combine like terms: 224 + -224 = 0
136 + -76x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(34 + -19x + x2) = 0

Factor a trinomial.
4((2 + -1x)(17 + -1x)) = 0

Ignore the factor 4.

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(17 + -1x)' equal to zero and attempt to solve:

Simplifying
17 + -1x = 0

Solving
17 + -1x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1x = 0 + -17
-1x = 0 + -17

Combine like terms: 0 + -17 = -17
-1x = -17

Divide each side by '-1'.
x = 17

Simplifying
x = 17
Solution
x = {2, 17}

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