40x-x^2=175

Solution for 40x-x^2=175 equation:

Simplifying
40x + -1x2 = 175

Solving
40x + -1x2 = 175

Solving for variable 'x'.

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

Combine like terms: 175 + -175 = 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}