72=x*(x+1)

Solution for 72=x*(x+1) equation:

Simplifying
72 = x(x + 1)

Reorder the terms:
72 = x(1 + x)
72 = (1 * x + x * x)
72 = (1x + x2)

Solving
72 = 1x + x2

Solving for variable 'x'.

Reorder the terms:
72 + -1x + -1x2 = 1x + -1x + x2 + -1x2

Combine like terms: 1x + -1x = 0
72 + -1x + -1x2 = 0 + x2 + -1x2
72 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
72 + -1x + -1x2 = 0

Factor a trinomial.
(8 + -1x)(9 + x) = 0

Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Subproblem 2
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

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

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

Simplifying
x = -9
Solution
x = {8, -9}