-4x(x-2)=-16+10

Solution for -4x(x-2)=-16+10 equation:

Simplifying
-4x(x + -2) = -16 + 10

Reorder the terms:
-4x(-2 + x) = -16 + 10
(-2 * -4x + x * -4x) = -16 + 10
(8x + -4x2) = -16 + 10

Combine like terms: -16 + 10 = -6
8x + -4x2 = -6

Solving
8x + -4x2 = -6

Solving for variable 'x'.

Reorder the terms:
6 + 8x + -4x2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + 8x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 4x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 4x + -2x2)' equal to zero and attempt to solve:

Simplifying
3 + 4x + -2x2 = 0

Solving
3 + 4x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-1.5 + -2x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -2x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -2x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -2x + x2 = 0 + 1.5
-2x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-2x + x2 = 1.5

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 = 1.5 + 1

Reorder the terms:
1 + -2x + x2 = 1.5 + 1

Combine like terms: 1.5 + 1 = 2.5
1 + -2x + x2 = 2.5

Factor a perfect square on the left side:
(x + -1)(x + -1) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(x + -1) equal to 1.58113883 and -1.58113883.

Subproblem 1
x + -1 = 1.58113883

Simplifying
x + -1 = 1.58113883

Reorder the terms:
-1 + x = 1.58113883

Solving
-1 + x = 1.58113883

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 = 1.58113883 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.58113883 + 1
x = 1.58113883 + 1

Combine like terms: 1.58113883 + 1 = 2.58113883
x = 2.58113883

Simplifying
x = 2.58113883

Subproblem 2
x + -1 = -1.58113883

Simplifying
x + -1 = -1.58113883

Reorder the terms:
-1 + x = -1.58113883

Solving
-1 + x = -1.58113883

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 = -1.58113883 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.58113883 + 1
x = -1.58113883 + 1

Combine like terms: -1.58113883 + 1 = -0.58113883
x = -0.58113883

Simplifying
x = -0.58113883

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.58113883, -0.58113883}
Solution
x = {2.58113883, -0.58113883}