x(x+1)=210

Solution for x(x+1)=210 equation:

Simplifying
x(x + 1) = 210

Reorder the terms:
x(1 + x) = 210
(1 * x + x * x) = 210
(1x + x2) = 210

Solving
1x + x2 = 210

Solving for variable 'x'.

Reorder the terms:
-210 + 1x + x2 = 210 + -210

Combine like terms: 210 + -210 = 0
-210 + 1x + x2 = 0

Factor a trinomial.
(-15 + -1x)(14 + -1x) = 0

Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve:

Simplifying
-15 + -1x = 0

Solving
-15 + -1x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1x = 0 + 15
-1x = 0 + 15

Combine like terms: 0 + 15 = 15
-1x = 15

Divide each side by '-1'.
x = -15

Simplifying
x = -15
Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14
Solution
x = {-15, 14}