x(x+1)=3906

Solution for x(x+1)=3906 equation:

Simplifying
x(x + 1) = 3906

Reorder the terms:
x(1 + x) = 3906
(1 * x + x * x) = 3906
(1x + x2) = 3906

Solving
1x + x2 = 3906

Solving for variable 'x'.

Reorder the terms:
-3906 + 1x + x2 = 3906 + -3906

Combine like terms: 3906 + -3906 = 0
-3906 + 1x + x2 = 0

Factor a trinomial.
(-63 + -1x)(62 + -1x) = 0

Subproblem 1
Set the factor '(-63 + -1x)' equal to zero and attempt to solve:

Simplifying
-63 + -1x = 0

Solving
-63 + -1x = 0

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

Add '63' to each side of the equation.
-63 + 63 + -1x = 0 + 63

Combine like terms: -63 + 63 = 0
0 + -1x = 0 + 63
-1x = 0 + 63

Combine like terms: 0 + 63 = 63
-1x = 63

Divide each side by '-1'.
x = -63

Simplifying
x = -63
Subproblem 2
Set the factor '(62 + -1x)' equal to zero and attempt to solve:

Simplifying
62 + -1x = 0

Solving
62 + -1x = 0

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

Add '-62' to each side of the equation.
62 + -62 + -1x = 0 + -62

Combine like terms: 62 + -62 = 0
0 + -1x = 0 + -62
-1x = 0 + -62

Combine like terms: 0 + -62 = -62
-1x = -62

Divide each side by '-1'.
x = 62

Simplifying
x = 62
Solution
x = {-63, 62}