(10000-10x)*(300-x)=1800000

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Solution for (10000-10x)*(300-x)=1800000 equation:


Simplifying
(10000 + -10x)(300 + -1x) = 1800000

Multiply (10000 + -10x) * (300 + -1x)
(10000(300 + -1x) + -10x * (300 + -1x)) = 1800000
((300 * 10000 + -1x * 10000) + -10x * (300 + -1x)) = 1800000
((3000000 + -10000x) + -10x * (300 + -1x)) = 1800000
(3000000 + -10000x + (300 * -10x + -1x * -10x)) = 1800000
(3000000 + -10000x + (-3000x + 10x2)) = 1800000

Combine like terms: -10000x + -3000x = -13000x
(3000000 + -13000x + 10x2) = 1800000

Solving
3000000 + -13000x + 10x2 = 1800000

Solving for variable 'x'.

Reorder the terms:
3000000 + -1800000 + -13000x + 10x2 = 1800000 + -1800000

Combine like terms: 3000000 + -1800000 = 1200000
1200000 + -13000x + 10x2 = 1800000 + -1800000

Combine like terms: 1800000 + -1800000 = 0
1200000 + -13000x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(120000 + -1300x + x2) = 0

Factor a trinomial.
10((100 + -1x)(1200 + -1x)) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(100 + -1x)' equal to zero and attempt to solve:

Simplifying
100 + -1x = 0

Solving
100 + -1x = 0

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

Add '-100' to each side of the equation.
100 + -100 + -1x = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -1x = 0 + -100
-1x = 0 + -100

Combine like terms: 0 + -100 = -100
-1x = -100

Divide each side by '-1'.
x = 100

Simplifying
x = 100

Subproblem 2
Set the factor '(1200 + -1x)' equal to zero and attempt to solve:

Simplifying
1200 + -1x = 0

Solving
1200 + -1x = 0

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

Add '-1200' to each side of the equation.
1200 + -1200 + -1x = 0 + -1200

Combine like terms: 1200 + -1200 = 0
0 + -1x = 0 + -1200
-1x = 0 + -1200

Combine like terms: 0 + -1200 = -1200
-1x = -1200

Divide each side by '-1'.
x = 1200

Simplifying
x = 1200
Solution
x = {100, 1200}

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