(x+1)(x)=5550

Solution for (x+1)(x)=5550 equation:

Simplifying
(x + 1)(x) = 5550

Reorder the terms:
(1 + x)(x) = 5550

Reorder the terms for easier multiplication:
x(1 + x) = 5550
(1 * x + x * x) = 5550
(1x + x2) = 5550

Solving
1x + x2 = 5550

Solving for variable 'x'.

Reorder the terms:
-5550 + 1x + x2 = 5550 + -5550

Combine like terms: 5550 + -5550 = 0
-5550 + 1x + x2 = 0

Factor a trinomial.
(-75 + -1x)(74 + -1x) = 0

Subproblem 1
Set the factor '(-75 + -1x)' equal to zero and attempt to solve:

Simplifying
-75 + -1x = 0

Solving
-75 + -1x = 0

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

Add '75' to each side of the equation.
-75 + 75 + -1x = 0 + 75

Combine like terms: -75 + 75 = 0
0 + -1x = 0 + 75
-1x = 0 + 75

Combine like terms: 0 + 75 = 75
-1x = 75

Divide each side by '-1'.
x = -75

Simplifying
x = -75
Subproblem 2
Set the factor '(74 + -1x)' equal to zero and attempt to solve:

Simplifying
74 + -1x = 0

Solving
74 + -1x = 0

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

Add '-74' to each side of the equation.
74 + -74 + -1x = 0 + -74

Combine like terms: 74 + -74 = 0
0 + -1x = 0 + -74
-1x = 0 + -74

Combine like terms: 0 + -74 = -74
-1x = -74

Divide each side by '-1'.
x = 74

Simplifying
x = 74
Solution
x = {-75, 74}