15000-500x+4x^2=0

Solution for 15000-500x+4x^2=0 equation:

Simplifying
15000 + -500x + 4x2 = 0

Solving
15000 + -500x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3750 + -125x + x2) = 0

Factor a trinomial.
4((50 + -1x)(75 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(50 + -1x)' equal to zero and attempt to solve:

Simplifying
50 + -1x = 0

Solving
50 + -1x = 0

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

Add '-50' to each side of the equation.
50 + -50 + -1x = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -1x = 0 + -50
-1x = 0 + -50

Combine like terms: 0 + -50 = -50
-1x = -50

Divide each side by '-1'.
x = 50

Simplifying
x = 50
Subproblem 2
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
Solution
x = {50, 75}