52-(x*x)+x=10

Solution for 52-(x*x)+x=10 equation:

Simplifying
52 + -1(x * x) + x = 10

Multiply x * x
52 + -1(x2) + x = 10

Reorder the terms:
52 + x + -1x2 = 10

Solving
52 + x + -1x2 = 10

Solving for variable 'x'.

Reorder the terms:
52 + -10 + x + -1x2 = 10 + -10

Combine like terms: 52 + -10 = 42
42 + x + -1x2 = 10 + -10

Combine like terms: 10 + -10 = 0
42 + x + -1x2 = 0

Factor a trinomial.
(7 + -1x)(6 + x) = 0

Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {7, -6}