100+500x-100x^2=700

Solution for 100+500x-100x^2=700 equation:

Simplifying
100 + 500x + -100x2 = 700

Solving
100 + 500x + -100x2 = 700

Solving for variable 'x'.

Reorder the terms:
100 + -700 + 500x + -100x2 = 700 + -700

Combine like terms: 100 + -700 = -600
-600 + 500x + -100x2 = 700 + -700

Combine like terms: 700 + -700 = 0
-600 + 500x + -100x2 = 0

Factor out the Greatest Common Factor (GCF), '100'.
100(-6 + 5x + -1x2) = 0

Factor a trinomial.
100((-3 + x)(2 + -1x)) = 0

Ignore the factor 100.
Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

Add '3' to each side of the equation.
-3 + 3 + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3
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 = {3, 2}