x(x+9)=52

Solution for x(x+9)=52 equation:

Simplifying
x(x + 9) = 52

Reorder the terms:
x(9 + x) = 52
(9 * x + x * x) = 52
(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.
(-13 + -1x)(4 + -1x) = 0

Subproblem 1
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
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 = {-13, 4}