400x+x^2+37500=0

Solution for 400x+x^2+37500=0 equation:

Simplifying
400x + x2 + 37500 = 0

Reorder the terms:
37500 + 400x + x2 = 0

Solving
37500 + 400x + x2 = 0

Solving for variable 'x'.

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

Subproblem 1
Set the factor '(250 + x)' equal to zero and attempt to solve:

Simplifying
250 + x = 0

Solving
250 + x = 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 + x = 0 + -250

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

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

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

Simplifying
150 + x = 0

Solving
150 + x = 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 + x = 0 + -150

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

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

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