-x^2+150x=5000

Solution for -x^2+150x=5000 equation:

Simplifying
-1x2 + 150x = 5000

Reorder the terms:
150x + -1x2 = 5000

Solving
150x + -1x2 = 5000

Solving for variable 'x'.

Reorder the terms:
-5000 + 150x + -1x2 = 5000 + -5000

Combine like terms: 5000 + -5000 = 0
-5000 + 150x + -1x2 = 0

Factor a trinomial.
(-100 + x)(50 + -1x) = 0

Subproblem 1
Set the factor '(-100 + x)' equal to zero and attempt to solve:

Simplifying
-100 + x = 0

Solving
-100 + x = 0

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

Add '100' to each side of the equation.
-100 + 100 + x = 0 + 100

Combine like terms: -100 + 100 = 0
0 + x = 0 + 100
x = 0 + 100

Combine like terms: 0 + 100 = 100
x = 100

Simplifying
x = 100
Subproblem 2
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
Solution
x = {100, 50}