x+(x-6)+x(x-9)=72

Solution for x+(x-6)+x(x-9)=72 equation:

Simplifying
x + (x + -6) + x(x + -9) = 72

Reorder the terms:
x + (-6 + x) + x(x + -9) = 72

Remove parenthesis around (-6 + x)
x + -6 + x + x(x + -9) = 72

Reorder the terms:
x + -6 + x + x(-9 + x) = 72
x + -6 + x + (-9 * x + x * x) = 72
x + -6 + x + (-9x + x2) = 72

Reorder the terms:
-6 + x + x + -9x + x2 = 72

Combine like terms: x + x = 2x
-6 + 2x + -9x + x2 = 72

Combine like terms: 2x + -9x = -7x
-6 + -7x + x2 = 72

Solving
-6 + -7x + x2 = 72

Solving for variable 'x'.

Reorder the terms:
-6 + -72 + -7x + x2 = 72 + -72

Combine like terms: -6 + -72 = -78
-78 + -7x + x2 = 72 + -72

Combine like terms: 72 + -72 = 0
-78 + -7x + x2 = 0

Factor a trinomial.
(-6 + -1x)(13 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 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 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
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 = {-6, 13}