(30-2x)(20-3x)=400

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Solution for (30-2x)(20-3x)=400 equation: 


Simplifying
(30 + -2x)(20 + -3x) = 400

Multiply (30 + -2x) * (20 + -3x)
(30(20 + -3x) + -2x * (20 + -3x)) = 400
((20 * 30 + -3x * 30) + -2x * (20 + -3x)) = 400
((600 + -90x) + -2x * (20 + -3x)) = 400
(600 + -90x + (20 * -2x + -3x * -2x)) = 400
(600 + -90x + (-40x + 6x2)) = 400

Combine like terms: -90x + -40x = -130x
(600 + -130x + 6x2) = 400

Solving
600 + -130x + 6x2 = 400

Solving for variable 'x'.

Reorder the terms:
600 + -400 + -130x + 6x2 = 400 + -400

Combine like terms: 600 + -400 = 200
200 + -130x + 6x2 = 400 + -400

Combine like terms: 400 + -400 = 0
200 + -130x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(100 + -65x + 3x2) = 0

Factor a trinomial.
2((5 + -3x)(20 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667

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 = {1.666666667, 20}

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