(40000+2000x)(25-x)+(40000+2000x)(5)=0

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Solution for (40000+2000x)(25-x)+(40000+2000x)(5)=0 equation:


Simplifying
(40000 + 2000x)(25 + -1x) + (40000 + 2000x)(5) = 0

Multiply (40000 + 2000x) * (25 + -1x)
(40000(25 + -1x) + 2000x * (25 + -1x)) + (40000 + 2000x)(5) = 0
((25 * 40000 + -1x * 40000) + 2000x * (25 + -1x)) + (40000 + 2000x)(5) = 0
((1000000 + -40000x) + 2000x * (25 + -1x)) + (40000 + 2000x)(5) = 0
(1000000 + -40000x + (25 * 2000x + -1x * 2000x)) + (40000 + 2000x)(5) = 0
(1000000 + -40000x + (50000x + -2000x2)) + (40000 + 2000x)(5) = 0

Combine like terms: -40000x + 50000x = 10000x
(1000000 + 10000x + -2000x2) + (40000 + 2000x)(5) = 0

Reorder the terms for easier multiplication:
1000000 + 10000x + -2000x2 + 5(40000 + 2000x) = 0
1000000 + 10000x + -2000x2 + (40000 * 5 + 2000x * 5) = 0
1000000 + 10000x + -2000x2 + (200000 + 10000x) = 0

Reorder the terms:
1000000 + 200000 + 10000x + 10000x + -2000x2 = 0

Combine like terms: 1000000 + 200000 = 1200000
1200000 + 10000x + 10000x + -2000x2 = 0

Combine like terms: 10000x + 10000x = 20000x
1200000 + 20000x + -2000x2 = 0

Solving
1200000 + 20000x + -2000x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2000'.
2000(600 + 10x + -1x2) = 0

Factor a trinomial.
2000((30 + -1x)(20 + x)) = 0

Ignore the factor 2000.

Subproblem 1

Set the factor '(30 + -1x)' equal to zero and attempt to solve: Simplifying 30 + -1x = 0 Solving 30 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + -1x = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -1x = 0 + -30 -1x = 0 + -30 Combine like terms: 0 + -30 = -30 -1x = -30 Divide each side by '-1'. x = 30 Simplifying x = 30

Subproblem 2

Set the factor '(20 + x)' equal to zero and attempt to solve: Simplifying 20 + x = 0 Solving 20 + x = 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 + x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + x = 0 + -20 x = 0 + -20 Combine like terms: 0 + -20 = -20 x = -20 Simplifying x = -20

Solution

x = {30, -20}

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