100x=-x^2+7500

Solution for 100x=-x^2+7500 equation:

Simplifying
100x = -1x2 + 7500

Reorder the terms:
100x = 7500 + -1x2

Solving
100x = 7500 + -1x2

Solving for variable 'x'.

Reorder the terms:
-7500 + 100x + x2 = 7500 + -1x2 + -7500 + x2

Reorder the terms:
-7500 + 100x + x2 = 7500 + -7500 + -1x2 + x2

Combine like terms: 7500 + -7500 = 0
-7500 + 100x + x2 = 0 + -1x2 + x2
-7500 + 100x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-7500 + 100x + x2 = 0

Factor a trinomial.
(-150 + -1x)(50 + -1x) = 0

Subproblem 1
Set the factor '(-150 + -1x)' equal to zero and attempt to solve:

Simplifying
-150 + -1x = 0

Solving
-150 + -1x = 0

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

Add '150' to each side of the equation.
-150 + 150 + -1x = 0 + 150

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

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

Divide each side by '-1'.
x = -150

Simplifying
x = -150
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 = {-150, 50}