(x*x)-9x=52

Solution for (x*x)-9x=52 equation:

Simplifying
(x * x) + -9x = 52

Multiply x * x
(x2) + -9x = 52
x2 + -9x = 52

Reorder the terms:
-9x + x2 = 52

Solving
-9x + x2 = 52

Solving for variable 'x'.

Reorder the terms:
-52 + -9x + x2 = 52 + -52

Combine like terms: 52 + -52 = 0
-52 + -9x + x2 = 0

Factor a trinomial.
(-4 + -1x)(13 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {-4, 13}