16=10+32x-16x^2

Solution for 16=10+32x-16x^2 equation:

Simplifying
16 = 10 + 32x + -16x2

Solving
16 = 10 + 32x + -16x2

Solving for variable 'x'.

Combine like terms: 16 + -10 = 6
6 + -32x + 16x2 = 10 + 32x + -16x2 + -10 + -32x + 16x2

Reorder the terms:
6 + -32x + 16x2 = 10 + -10 + 32x + -32x + -16x2 + 16x2

Combine like terms: 10 + -10 = 0
6 + -32x + 16x2 = 0 + 32x + -32x + -16x2 + 16x2
6 + -32x + 16x2 = 32x + -32x + -16x2 + 16x2

Combine like terms: 32x + -32x = 0
6 + -32x + 16x2 = 0 + -16x2 + 16x2
6 + -32x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
6 + -32x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -16x + 8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -16x + 8x2)' equal to zero and attempt to solve:

Simplifying
3 + -16x + 8x2 = 0

Solving
3 + -16x + 8x2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
0.375 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + -2x + -0.375 + x2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + -2x + x2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + -2x + x2 = 0 + -0.375
-2x + x2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
-2x + x2 = -0.375

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -0.375 + 1

Reorder the terms:
1 + -2x + x2 = -0.375 + 1

Combine like terms: -0.375 + 1 = 0.625
1 + -2x + x2 = 0.625

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.625

Calculate the square root of the right side: 0.790569415

Break this problem into two subproblems by setting 
(x + -1) equal to 0.790569415 and -0.790569415.

Subproblem 1
x + -1 = 0.790569415

Simplifying
x + -1 = 0.790569415

Reorder the terms:
-1 + x = 0.790569415

Solving
-1 + x = 0.790569415

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 0.790569415 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0.790569415 + 1
x = 0.790569415 + 1

Combine like terms: 0.790569415 + 1 = 1.790569415
x = 1.790569415

Simplifying
x = 1.790569415

Subproblem 2
x + -1 = -0.790569415

Simplifying
x + -1 = -0.790569415

Reorder the terms:
-1 + x = -0.790569415

Solving
-1 + x = -0.790569415

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -0.790569415 + 1

Combine like terms: -1 + 1 = 0
0 + x = -0.790569415 + 1
x = -0.790569415 + 1

Combine like terms: -0.790569415 + 1 = 0.209430585
x = 0.209430585

Simplifying
x = 0.209430585

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.790569415, 0.209430585}
Solution
x = {1.790569415, 0.209430585}