[40000+5000x][16-x]+[40000+5000x][4.00]=

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Solution for [40000+5000x][16-x]+[40000+5000x][4.00]= equation: 


Simplifying
[40000 + 5000x][16 + -1x] + [40000 + 5000x][4.00] = 0

Multiply [40000 + 5000x] * [16 + -1x]
[40000[16 + -1x] + 5000x * [16 + -1x]] + [40000 + 5000x][4.00] = 0
[[16 * 40000 + -1x * 40000] + 5000x * [16 + -1x]] + [40000 + 5000x][4.00] = 0
[[640000 + -40000x] + 5000x * [16 + -1x]] + [40000 + 5000x][4.00] = 0
[640000 + -40000x + [16 * 5000x + -1x * 5000x]] + [40000 + 5000x][4.00] = 0
[640000 + -40000x + [80000x + -5000x2]] + [40000 + 5000x][4.00] = 0

Combine like terms: -40000x + 80000x = 40000x
[640000 + 40000x + -5000x2] + [40000 + 5000x][4.00] = 0

Reorder the terms for easier multiplication:
640000 + 40000x + -5000x2 + 4.00[40000 + 5000x] = 0
640000 + 40000x + -5000x2 + [40000 * 4.00 + 5000x * 4.00] = 0
640000 + 40000x + -5000x2 + [160000 + 20000x] = 0

Reorder the terms:
640000 + 160000 + 40000x + 20000x + -5000x2 = 0

Combine like terms: 640000 + 160000 = 800000
800000 + 40000x + 20000x + -5000x2 = 0

Combine like terms: 40000x + 20000x = 60000x
800000 + 60000x + -5000x2 = 0

Solving
800000 + 60000x + -5000x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5000'.
5000(160 + 12x + -1x2) = 0

Factor a trinomial.
5000((20 + -1x)(8 + x)) = 0

Ignore the factor 5000.

Subproblem 1
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

Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Solution
x = {20, -8}

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