x^2-75x+2000=50x-500

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Solution for x^2-75x+2000=50x-500 equation:


Simplifying
x2 + -75x + 2000 = 50x + -500

Reorder the terms:
2000 + -75x + x2 = 50x + -500

Reorder the terms:
2000 + -75x + x2 = -500 + 50x

Solving
2000 + -75x + x2 = -500 + 50x

Solving for variable 'x'.

Reorder the terms:
2000 + 500 + -75x + -50x + x2 = -500 + 50x + 500 + -50x

Combine like terms: 2000 + 500 = 2500
2500 + -75x + -50x + x2 = -500 + 50x + 500 + -50x

Combine like terms: -75x + -50x = -125x
2500 + -125x + x2 = -500 + 50x + 500 + -50x

Reorder the terms:
2500 + -125x + x2 = -500 + 500 + 50x + -50x

Combine like terms: -500 + 500 = 0
2500 + -125x + x2 = 0 + 50x + -50x
2500 + -125x + x2 = 50x + -50x

Combine like terms: 50x + -50x = 0
2500 + -125x + x2 = 0

Factor a trinomial.
(25 + -1x)(100 + -1x) = 0


Subproblem 1
Set the factor '(25 + -1x)' equal to zero and attempt to solve:

Simplifying
25 + -1x = 0

Solving
25 + -1x = 0

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

Add '-25' to each side of the equation.
25 + -25 + -1x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -1x = 0 + -25
-1x = 0 + -25

Combine like terms: 0 + -25 = -25
-1x = -25

Divide each side by '-1'.
x = 25

Simplifying
x = 25

Subproblem 2
Set the factor '(100 + -1x)' equal to zero and attempt to solve:

Simplifying
100 + -1x = 0

Solving
100 + -1x = 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 + -1x = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -1x = 0 + -100
-1x = 0 + -100

Combine like terms: 0 + -100 = -100
-1x = -100

Divide each side by '-1'.
x = 100

Simplifying
x = 100
Solution
x = {25, 100}

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