(1000+200x)(100-3x)=

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Solution for (1000+200x)(100-3x)= equation: 


Simplifying
(1000 + 200x)(100 + -3x) = 0

Multiply (1000 + 200x) * (100 + -3x)
(1000(100 + -3x) + 200x * (100 + -3x)) = 0
((100 * 1000 + -3x * 1000) + 200x * (100 + -3x)) = 0
((100000 + -3000x) + 200x * (100 + -3x)) = 0
(100000 + -3000x + (100 * 200x + -3x * 200x)) = 0
(100000 + -3000x + (20000x + -600x2)) = 0

Combine like terms: -3000x + 20000x = 17000x
(100000 + 17000x + -600x2) = 0

Solving
100000 + 17000x + -600x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '200'.
200(500 + 85x + -3x2) = 0

Factor a trinomial.
200((100 + -3x)(5 + x)) = 0

Ignore the factor 200.

Subproblem 1
Set the factor '(100 + -3x)' equal to zero and attempt to solve:

Simplifying
100 + -3x = 0

Solving
100 + -3x = 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 + -3x = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -3x = 0 + -100
-3x = 0 + -100

Combine like terms: 0 + -100 = -100
-3x = -100

Divide each side by '-3'.
x = 33.33333333

Simplifying
x = 33.33333333

Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

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

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

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

Simplifying
x = -5
Solution
x = {33.33333333, -5}

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