x^2+15x=4500

Solution for x^2+15x=4500 equation:

Simplifying
x2 + 15x = 4500

Reorder the terms:
15x + x2 = 4500

Solving
15x + x2 = 4500

Solving for variable 'x'.

Reorder the terms:
-4500 + 15x + x2 = 4500 + -4500

Combine like terms: 4500 + -4500 = 0
-4500 + 15x + x2 = 0

Factor a trinomial.
(-75 + -1x)(60 + -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 '(60 + -1x)' equal to zero and attempt to solve:

Simplifying
60 + -1x = 0

Solving
60 + -1x = 0

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

Add '-60' to each side of the equation.
60 + -60 + -1x = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -1x = 0 + -60
-1x = 0 + -60

Combine like terms: 0 + -60 = -60
-1x = -60

Divide each side by '-1'.
x = 60

Simplifying
x = 60
Solution
x = {-75, 60}