10+3(x-2)x=16

Solution for 10+3(x-2)x=16 equation:

Simplifying
10 + 3(x + -2) * x = 16

Reorder the terms:
10 + 3(-2 + x) * x = 16

Reorder the terms for easier multiplication:
10 + 3x(-2 + x) = 16
10 + (-2 * 3x + x * 3x) = 16
10 + (-6x + 3x2) = 16

Solving
10 + -6x + 3x2 = 16

Solving for variable 'x'.

Reorder the terms:
10 + -16 + -6x + 3x2 = 16 + -16

Combine like terms: 10 + -16 = -6
-6 + -6x + 3x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-6 + -6x + 3x2 = 0

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

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

Simplifying
-2 + -2x + x2 = 0

Solving
-2 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 2 + 1

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

Combine like terms: 2 + 1 = 3
1 + -2x + x2 = 3

Factor a perfect square on the left side:
(x + -1)(x + -1) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + -1) equal to 1.732050808 and -1.732050808.

Subproblem 1
x + -1 = 1.732050808

Simplifying
x + -1 = 1.732050808

Reorder the terms:
-1 + x = 1.732050808

Solving
-1 + x = 1.732050808

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 = 1.732050808 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.732050808 + 1
x = 1.732050808 + 1

Combine like terms: 1.732050808 + 1 = 2.732050808
x = 2.732050808

Simplifying
x = 2.732050808

Subproblem 2
x + -1 = -1.732050808

Simplifying
x + -1 = -1.732050808

Reorder the terms:
-1 + x = -1.732050808

Solving
-1 + x = -1.732050808

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 = -1.732050808 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.732050808 + 1
x = -1.732050808 + 1

Combine like terms: -1.732050808 + 1 = -0.732050808
x = -0.732050808

Simplifying
x = -0.732050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.732050808, -0.732050808}
Solution
x = {2.732050808, -0.732050808}