(30-2x)*(20-2x)=416

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Solution for (30-2x)*(20-2x)=416 equation: 


Simplifying
(30 + -2x)(20 + -2x) = 416

Multiply (30 + -2x) * (20 + -2x)
(30(20 + -2x) + -2x * (20 + -2x)) = 416
((20 * 30 + -2x * 30) + -2x * (20 + -2x)) = 416
((600 + -60x) + -2x * (20 + -2x)) = 416
(600 + -60x + (20 * -2x + -2x * -2x)) = 416
(600 + -60x + (-40x + 4x2)) = 416

Combine like terms: -60x + -40x = -100x
(600 + -100x + 4x2) = 416

Solving
600 + -100x + 4x2 = 416

Solving for variable 'x'.

Reorder the terms:
600 + -416 + -100x + 4x2 = 416 + -416

Combine like terms: 600 + -416 = 184
184 + -100x + 4x2 = 416 + -416

Combine like terms: 416 + -416 = 0
184 + -100x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(46 + -25x + x2) = 0

Factor a trinomial.
4((2 + -1x)(23 + -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 '(23 + -1x)' equal to zero and attempt to solve:

Simplifying
23 + -1x = 0

Solving
23 + -1x = 0

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

Add '-23' to each side of the equation.
23 + -23 + -1x = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -1x = 0 + -23
-1x = 0 + -23

Combine like terms: 0 + -23 = -23
-1x = -23

Divide each side by '-1'.
x = 23

Simplifying
x = 23
Solution
x = {2, 23}

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