300=100+300x-100x^2

Solution for 300=100+300x-100x^2 equation:

Simplifying
300 = 100 + 300x + -100x2

Solving
300 = 100 + 300x + -100x2

Solving for variable 'x'.

Combine like terms: 300 + -100 = 200
200 + -300x + 100x2 = 100 + 300x + -100x2 + -100 + -300x + 100x2

Reorder the terms:
200 + -300x + 100x2 = 100 + -100 + 300x + -300x + -100x2 + 100x2

Combine like terms: 100 + -100 = 0
200 + -300x + 100x2 = 0 + 300x + -300x + -100x2 + 100x2
200 + -300x + 100x2 = 300x + -300x + -100x2 + 100x2

Combine like terms: 300x + -300x = 0
200 + -300x + 100x2 = 0 + -100x2 + 100x2
200 + -300x + 100x2 = -100x2 + 100x2

Combine like terms: -100x2 + 100x2 = 0
200 + -300x + 100x2 = 0

Factor out the Greatest Common Factor (GCF), '100'.
100(2 + -3x + x2) = 0

Factor a trinomial.
100((1 + -1x)(2 + -1x)) = 0

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {1, 2}