125x^2+5000x-62500=0

Solution for 125x^2+5000x-62500=0 equation:

Simplifying
125x2 + 5000x + -62500 = 0

Reorder the terms:
-62500 + 5000x + 125x2 = 0

Solving
-62500 + 5000x + 125x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '125'.
125(-500 + 40x + x2) = 0

Factor a trinomial.
125((-50 + -1x)(10 + -1x)) = 0

Ignore the factor 125.
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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-50, 10}