-16x^2+208x+55=407

Solution for -16x^2+208x+55=407 equation:

Simplifying
-16x2 + 208x + 55 = 407

Reorder the terms:
55 + 208x + -16x2 = 407

Solving
55 + 208x + -16x2 = 407

Solving for variable 'x'.

Reorder the terms:
55 + -407 + 208x + -16x2 = 407 + -407

Combine like terms: 55 + -407 = -352
-352 + 208x + -16x2 = 407 + -407

Combine like terms: 407 + -407 = 0
-352 + 208x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-22 + 13x + -1x2) = 0

Factor a trinomial.
16((-11 + x)(2 + -1x)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(-11 + x)' equal to zero and attempt to solve:

Simplifying
-11 + x = 0

Solving
-11 + x = 0

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

Add '11' to each side of the equation.
-11 + 11 + x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + x = 0 + 11
x = 0 + 11

Combine like terms: 0 + 11 = 11
x = 11

Simplifying
x = 11
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 = {11, 2}