101=-16x^2+80x+5

Solution for 101=-16x^2+80x+5 equation:

Simplifying
101 = -16x2 + 80x + 5

Reorder the terms:
101 = 5 + 80x + -16x2

Solving
101 = 5 + 80x + -16x2

Solving for variable 'x'.

Combine like terms: 101 + -5 = 96
96 + -80x + 16x2 = 5 + 80x + -16x2 + -5 + -80x + 16x2

Reorder the terms:
96 + -80x + 16x2 = 5 + -5 + 80x + -80x + -16x2 + 16x2

Combine like terms: 5 + -5 = 0
96 + -80x + 16x2 = 0 + 80x + -80x + -16x2 + 16x2
96 + -80x + 16x2 = 80x + -80x + -16x2 + 16x2

Combine like terms: 80x + -80x = 0
96 + -80x + 16x2 = 0 + -16x2 + 16x2
96 + -80x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
96 + -80x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(6 + -5x + x2) = 0

Factor a trinomial.
16((2 + -1x)(3 + -1x)) = 0

Ignore the factor 16.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {2, 3}