300=-2x^2+40x+100

Solution for 300=-2x^2+40x+100 equation:

Simplifying
300 = -2x2 + 40x + 100

Reorder the terms:
300 = 100 + 40x + -2x2

Solving
300 = 100 + 40x + -2x2

Solving for variable 'x'.

Combine like terms: 300 + -100 = 200
200 + -40x + 2x2 = 100 + 40x + -2x2 + -100 + -40x + 2x2

Reorder the terms:
200 + -40x + 2x2 = 100 + -100 + 40x + -40x + -2x2 + 2x2

Combine like terms: 100 + -100 = 0
200 + -40x + 2x2 = 0 + 40x + -40x + -2x2 + 2x2
200 + -40x + 2x2 = 40x + -40x + -2x2 + 2x2

Combine like terms: 40x + -40x = 0
200 + -40x + 2x2 = 0 + -2x2 + 2x2
200 + -40x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
200 + -40x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(100 + -20x + x2) = 0

Factor a trinomial.
2((10 + -1x)(10 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {10, 10}