10x+175=-x^2+50x

Solution for 10x+175=-x^2+50x equation:

Simplifying
10x + 175 = -1x2 + 50x

Reorder the terms:
175 + 10x = -1x2 + 50x

Reorder the terms:
175 + 10x = 50x + -1x2

Solving
175 + 10x = 50x + -1x2

Solving for variable 'x'.

Combine like terms: 10x + -50x = -40x
175 + -40x + x2 = 50x + -1x2 + -50x + x2

Reorder the terms:
175 + -40x + x2 = 50x + -50x + -1x2 + x2

Combine like terms: 50x + -50x = 0
175 + -40x + x2 = 0 + -1x2 + x2
175 + -40x + x2 = -1x2 + x2

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

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

Subproblem 1
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
Subproblem 2
Set the factor '(35 + -1x)' equal to zero and attempt to solve:

Simplifying
35 + -1x = 0

Solving
35 + -1x = 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 + -1x = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -1x = 0 + -35
-1x = 0 + -35

Combine like terms: 0 + -35 = -35
-1x = -35

Divide each side by '-1'.
x = 35

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