x(x-1)=15006

Solution for x(x-1)=15006 equation:

Simplifying
x(x + -1) = 15006

Reorder the terms:
x(-1 + x) = 15006
(-1 * x + x * x) = 15006
(-1x + x2) = 15006

Solving
-1x + x2 = 15006

Solving for variable 'x'.

Reorder the terms:
-15006 + -1x + x2 = 15006 + -15006

Combine like terms: 15006 + -15006 = 0
-15006 + -1x + x2 = 0

Factor a trinomial.
(-122 + -1x)(123 + -1x) = 0

Subproblem 1
Set the factor '(-122 + -1x)' equal to zero and attempt to solve:

Simplifying
-122 + -1x = 0

Solving
-122 + -1x = 0

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

Add '122' to each side of the equation.
-122 + 122 + -1x = 0 + 122

Combine like terms: -122 + 122 = 0
0 + -1x = 0 + 122
-1x = 0 + 122

Combine like terms: 0 + 122 = 122
-1x = 122

Divide each side by '-1'.
x = -122

Simplifying
x = -122
Subproblem 2
Set the factor '(123 + -1x)' equal to zero and attempt to solve:

Simplifying
123 + -1x = 0

Solving
123 + -1x = 0

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

Add '-123' to each side of the equation.
123 + -123 + -1x = 0 + -123

Combine like terms: 123 + -123 = 0
0 + -1x = 0 + -123
-1x = 0 + -123

Combine like terms: 0 + -123 = -123
-1x = -123

Divide each side by '-1'.
x = 123

Simplifying
x = 123
Solution
x = {-122, 123}