x(x+1)=342

Solution for x(x+1)=342 equation:

Simplifying
x(x + 1) = 342

Reorder the terms:
x(1 + x) = 342
(1 * x + x * x) = 342
(1x + x2) = 342

Solving
1x + x2 = 342

Solving for variable 'x'.

Reorder the terms:
-342 + 1x + x2 = 342 + -342

Combine like terms: 342 + -342 = 0
-342 + 1x + x2 = 0

Factor a trinomial.
(-19 + -1x)(18 + -1x) = 0

Subproblem 1
Set the factor '(-19 + -1x)' equal to zero and attempt to solve:

Simplifying
-19 + -1x = 0

Solving
-19 + -1x = 0

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

Add '19' to each side of the equation.
-19 + 19 + -1x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -1x = 0 + 19
-1x = 0 + 19

Combine like terms: 0 + 19 = 19
-1x = 19

Divide each side by '-1'.
x = -19

Simplifying
x = -19
Subproblem 2
Set the factor '(18 + -1x)' equal to zero and attempt to solve:

Simplifying
18 + -1x = 0

Solving
18 + -1x = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1x = 0 + -18
-1x = 0 + -18

Combine like terms: 0 + -18 = -18
-1x = -18

Divide each side by '-1'.
x = 18

Simplifying
x = 18
Solution
x = {-19, 18}