53x-x^2=196

Solution for 53x-x^2=196 equation:

Simplifying
53x + -1x2 = 196

Solving
53x + -1x2 = 196

Solving for variable 'x'.

Reorder the terms:
-196 + 53x + -1x2 = 196 + -196

Combine like terms: 196 + -196 = 0
-196 + 53x + -1x2 = 0

Factor a trinomial.
(-49 + x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-49 + x)' equal to zero and attempt to solve:

Simplifying
-49 + x = 0

Solving
-49 + x = 0

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

Add '49' to each side of the equation.
-49 + 49 + x = 0 + 49

Combine like terms: -49 + 49 = 0
0 + x = 0 + 49
x = 0 + 49

Combine like terms: 0 + 49 = 49
x = 49

Simplifying
x = 49
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {49, 4}