(10+x)(500-20x)=6000

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Solution for (10+x)(500-20x)=6000 equation:


Simplifying
(10 + x)(500 + -20x) = 6000

Multiply (10 + x) * (500 + -20x)
(10(500 + -20x) + x(500 + -20x)) = 6000
((500 * 10 + -20x * 10) + x(500 + -20x)) = 6000
((5000 + -200x) + x(500 + -20x)) = 6000
(5000 + -200x + (500 * x + -20x * x)) = 6000
(5000 + -200x + (500x + -20x2)) = 6000

Combine like terms: -200x + 500x = 300x
(5000 + 300x + -20x2) = 6000

Solving
5000 + 300x + -20x2 = 6000

Solving for variable 'x'.

Reorder the terms:
5000 + -6000 + 300x + -20x2 = 6000 + -6000

Combine like terms: 5000 + -6000 = -1000
-1000 + 300x + -20x2 = 6000 + -6000

Combine like terms: 6000 + -6000 = 0
-1000 + 300x + -20x2 = 0

Factor out the Greatest Common Factor (GCF), '20'.
20(-50 + 15x + -1x2) = 0

Factor a trinomial.
20((-10 + x)(5 + -1x)) = 0

Ignore the factor 20.

Subproblem 1

Set the factor '(-10 + x)' equal to zero and attempt to solve: Simplifying -10 + x = 0 Solving -10 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + x = 0 + 10 x = 0 + 10 Combine like terms: 0 + 10 = 10 x = 10 Simplifying x = 10

Subproblem 2

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {10, 5}

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