x(x-1)=380

Solution for x(x-1)=380 equation:

Simplifying
x(x + -1) = 380

Reorder the terms:
x(-1 + x) = 380
(-1 * x + x * x) = 380
(-1x + x2) = 380

Solving
-1x + x2 = 380

Solving for variable 'x'.

Reorder the terms:
-380 + -1x + x2 = 380 + -380

Combine like terms: 380 + -380 = 0
-380 + -1x + x2 = 0

Factor a trinomial.
(-19 + -1x)(20 + -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 '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Solution
x = {-19, 20}