(2x+5)(x+20)=10000

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Solution for (2x+5)(x+20)=10000 equation: 


Simplifying
(2x + 5)(x + 20) = 10000

Reorder the terms:
(5 + 2x)(x + 20) = 10000

Reorder the terms:
(5 + 2x)(20 + x) = 10000

Multiply (5 + 2x) * (20 + x)
(5(20 + x) + 2x * (20 + x)) = 10000
((20 * 5 + x * 5) + 2x * (20 + x)) = 10000
((100 + 5x) + 2x * (20 + x)) = 10000
(100 + 5x + (20 * 2x + x * 2x)) = 10000
(100 + 5x + (40x + 2x2)) = 10000

Combine like terms: 5x + 40x = 45x
(100 + 45x + 2x2) = 10000

Solving
100 + 45x + 2x2 = 10000

Solving for variable 'x'.

Reorder the terms:
100 + -10000 + 45x + 2x2 = 10000 + -10000

Combine like terms: 100 + -10000 = -9900
-9900 + 45x + 2x2 = 10000 + -10000

Combine like terms: 10000 + -10000 = 0
-9900 + 45x + 2x2 = 0

Factor a trinomial.
(-165 + -2x)(60 + -1x) = 0


Subproblem 1
Set the factor '(-165 + -2x)' equal to zero and attempt to solve:

Simplifying
-165 + -2x = 0

Solving
-165 + -2x = 0

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

Add '165' to each side of the equation.
-165 + 165 + -2x = 0 + 165

Combine like terms: -165 + 165 = 0
0 + -2x = 0 + 165
-2x = 0 + 165

Combine like terms: 0 + 165 = 165
-2x = 165

Divide each side by '-2'.
x = -82.5

Simplifying
x = -82.5

Subproblem 2
Set the factor '(60 + -1x)' equal to zero and attempt to solve:

Simplifying
60 + -1x = 0

Solving
60 + -1x = 0

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

Add '-60' to each side of the equation.
60 + -60 + -1x = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -1x = 0 + -60
-1x = 0 + -60

Combine like terms: 0 + -60 = -60
-1x = -60

Divide each side by '-1'.
x = 60

Simplifying
x = 60
Solution
x = {-82.5, 60}

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