x^2-400x=-37500

Solution for x^2-400x=-37500 equation:

Simplifying
x2 + -400x = -37500

Reorder the terms:
-400x + x2 = -37500

Solving
-400x + x2 = -37500

Solving for variable 'x'.

Reorder the terms:
37500 + -400x + x2 = -37500 + 37500

Combine like terms: -37500 + 37500 = 0
37500 + -400x + x2 = 0

Factor a trinomial.
(150 + -1x)(250 + -1x) = 0

Subproblem 1
Set the factor '(150 + -1x)' equal to zero and attempt to solve:

Simplifying
150 + -1x = 0

Solving
150 + -1x = 0

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

Add '-150' to each side of the equation.
150 + -150 + -1x = 0 + -150

Combine like terms: 150 + -150 = 0
0 + -1x = 0 + -150
-1x = 0 + -150

Combine like terms: 0 + -150 = -150
-1x = -150

Divide each side by '-1'.
x = 150

Simplifying
x = 150
Subproblem 2
Set the factor '(250 + -1x)' equal to zero and attempt to solve:

Simplifying
250 + -1x = 0

Solving
250 + -1x = 0

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

Add '-250' to each side of the equation.
250 + -250 + -1x = 0 + -250

Combine like terms: 250 + -250 = 0
0 + -1x = 0 + -250
-1x = 0 + -250

Combine like terms: 0 + -250 = -250
-1x = -250

Divide each side by '-1'.
x = 250

Simplifying
x = 250
Solution
x = {150, 250}