x^2-45x=9000

Solution for x^2-45x=9000 equation:

Simplifying
x2 + -45x = 9000

Reorder the terms:
-45x + x2 = 9000

Solving
-45x + x2 = 9000

Solving for variable 'x'.

Reorder the terms:
-9000 + -45x + x2 = 9000 + -9000

Combine like terms: 9000 + -9000 = 0
-9000 + -45x + x2 = 0

Factor a trinomial.
(-75 + -1x)(120 + -1x) = 0

Subproblem 1
Set the factor '(-75 + -1x)' equal to zero and attempt to solve:

Simplifying
-75 + -1x = 0

Solving
-75 + -1x = 0

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

Add '75' to each side of the equation.
-75 + 75 + -1x = 0 + 75

Combine like terms: -75 + 75 = 0
0 + -1x = 0 + 75
-1x = 0 + 75

Combine like terms: 0 + 75 = 75
-1x = 75

Divide each side by '-1'.
x = -75

Simplifying
x = -75
Subproblem 2
Set the factor '(120 + -1x)' equal to zero and attempt to solve:

Simplifying
120 + -1x = 0

Solving
120 + -1x = 0

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

Add '-120' to each side of the equation.
120 + -120 + -1x = 0 + -120

Combine like terms: 120 + -120 = 0
0 + -1x = 0 + -120
-1x = 0 + -120

Combine like terms: 0 + -120 = -120
-1x = -120

Divide each side by '-1'.
x = 120

Simplifying
x = 120
Solution
x = {-75, 120}