75x+2600=225x-x^2

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Solution for 75x+2600=225x-x^2 equation:


Simplifying
75x + 2600 = 225x + -1x2

Reorder the terms:
2600 + 75x = 225x + -1x2

Solving
2600 + 75x = 225x + -1x2

Solving for variable 'x'.

Combine like terms: 75x + -225x = -150x
2600 + -150x + x2 = 225x + -1x2 + -225x + x2

Reorder the terms:
2600 + -150x + x2 = 225x + -225x + -1x2 + x2

Combine like terms: 225x + -225x = 0
2600 + -150x + x2 = 0 + -1x2 + x2
2600 + -150x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
2600 + -150x + x2 = 0

Factor a trinomial.
(20 + -1x)(130 + -1x) = 0

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 '(130 + -1x)' equal to zero and attempt to solve: Simplifying 130 + -1x = 0 Solving 130 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-130' to each side of the equation. 130 + -130 + -1x = 0 + -130 Combine like terms: 130 + -130 = 0 0 + -1x = 0 + -130 -1x = 0 + -130 Combine like terms: 0 + -130 = -130 -1x = -130 Divide each side by '-1'. x = 130 Simplifying x = 130

Solution

x = {20, 130}

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