0=x(120-x)-50x

Solution for 0=x(120-x)-50x equation:

Simplifying
0 = x(120 + -1x) + -50x
0 = (120 * x + -1x * x) + -50x
0 = (120x + -1x2) + -50x

Reorder the terms:
0 = 120x + -50x + -1x2

Combine like terms: 120x + -50x = 70x
0 = 70x + -1x2

Solving
0 = 70x + -1x2

Solving for variable 'x'.
Remove the zero:
-70x + x2 = 70x + -1x2 + -70x + x2

Reorder the terms:
-70x + x2 = 70x + -70x + -1x2 + x2

Combine like terms: 70x + -70x = 0
-70x + x2 = 0 + -1x2 + x2
-70x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-70x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-70 + x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-70 + x)' equal to zero and attempt to solve:

Simplifying
-70 + x = 0

Solving
-70 + x = 0

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

Add '70' to each side of the equation.
-70 + 70 + x = 0 + 70

Combine like terms: -70 + 70 = 0
0 + x = 0 + 70
x = 0 + 70

Combine like terms: 0 + 70 = 70
x = 70

Simplifying
x = 70
Solution
x = {0, 70}