10x(10-x)=250

Solution for 10x(10-x)=250 equation:

Simplifying
10x(10 + -1x) = 250
(10 * 10x + -1x * 10x) = 250
(100x + -10x2) = 250

Solving
100x + -10x2 = 250

Solving for variable 'x'.

Reorder the terms:
-250 + 100x + -10x2 = 250 + -250

Combine like terms: 250 + -250 = 0
-250 + 100x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-25 + 10x + -1x2) = 0

Factor a trinomial.
10((-5 + x)(5 + -1x)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {5, 5}