-x^2+35x+100=-5x+275

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Solution for -x^2+35x+100=-5x+275 equation: 


Simplifying
-1x2 + 35x + 100 = -5x + 275

Reorder the terms:
100 + 35x + -1x2 = -5x + 275

Reorder the terms:
100 + 35x + -1x2 = 275 + -5x

Solving
100 + 35x + -1x2 = 275 + -5x

Solving for variable 'x'.

Reorder the terms:
100 + -275 + 35x + 5x + -1x2 = 275 + -5x + -275 + 5x

Combine like terms: 100 + -275 = -175
-175 + 35x + 5x + -1x2 = 275 + -5x + -275 + 5x

Combine like terms: 35x + 5x = 40x
-175 + 40x + -1x2 = 275 + -5x + -275 + 5x

Reorder the terms:
-175 + 40x + -1x2 = 275 + -275 + -5x + 5x

Combine like terms: 275 + -275 = 0
-175 + 40x + -1x2 = 0 + -5x + 5x
-175 + 40x + -1x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-175 + 40x + -1x2 = 0

Factor a trinomial.
(-35 + x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-35 + x)' equal to zero and attempt to solve:

Simplifying
-35 + x = 0

Solving
-35 + x = 0

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

Add '35' to each side of the equation.
-35 + 35 + x = 0 + 35

Combine like terms: -35 + 35 = 0
0 + x = 0 + 35
x = 0 + 35

Combine like terms: 0 + 35 = 35
x = 35

Simplifying
x = 35

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {35, 5}

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