4x-5(2-x)=3x(x-6)-16

Solution for 4x-5(2-x)=3x(x-6)-16 equation:

Simplifying
4x + -5(2 + -1x) = 3x(x + -6) + -16
4x + (2 * -5 + -1x * -5) = 3x(x + -6) + -16
4x + (-10 + 5x) = 3x(x + -6) + -16

Reorder the terms:
-10 + 4x + 5x = 3x(x + -6) + -16

Combine like terms: 4x + 5x = 9x
-10 + 9x = 3x(x + -6) + -16

Reorder the terms:
-10 + 9x = 3x(-6 + x) + -16
-10 + 9x = (-6 * 3x + x * 3x) + -16
-10 + 9x = (-18x + 3x2) + -16

Reorder the terms:
-10 + 9x = -16 + -18x + 3x2

Solving
-10 + 9x = -16 + -18x + 3x2

Solving for variable 'x'.

Reorder the terms:
-10 + 16 + 9x + 18x + -3x2 = -16 + -18x + 3x2 + 16 + 18x + -3x2

Combine like terms: -10 + 16 = 6
6 + 9x + 18x + -3x2 = -16 + -18x + 3x2 + 16 + 18x + -3x2

Combine like terms: 9x + 18x = 27x
6 + 27x + -3x2 = -16 + -18x + 3x2 + 16 + 18x + -3x2

Reorder the terms:
6 + 27x + -3x2 = -16 + 16 + -18x + 18x + 3x2 + -3x2

Combine like terms: -16 + 16 = 0
6 + 27x + -3x2 = 0 + -18x + 18x + 3x2 + -3x2
6 + 27x + -3x2 = -18x + 18x + 3x2 + -3x2

Combine like terms: -18x + 18x = 0
6 + 27x + -3x2 = 0 + 3x2 + -3x2
6 + 27x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
6 + 27x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 9x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + 9x + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + 9x + -1x2 = 0

Solving
2 + 9x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2 + -9x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -9x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -9x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -9x + x2 = 0 + 2
-9x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-9x + x2 = 2

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 2 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 2 + 20.25

Combine like terms: 2 + 20.25 = 22.25
20.25 + -9x + x2 = 22.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(x + -4.5) equal to 4.716990566 and -4.716990566.

Subproblem 1
x + -4.5 = 4.716990566

Simplifying
x + -4.5 = 4.716990566

Reorder the terms:
-4.5 + x = 4.716990566

Solving
-4.5 + x = 4.716990566

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 4.716990566 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 4.716990566 + 4.5
x = 4.716990566 + 4.5

Combine like terms: 4.716990566 + 4.5 = 9.216990566
x = 9.216990566

Simplifying
x = 9.216990566

Subproblem 2
x + -4.5 = -4.716990566

Simplifying
x + -4.5 = -4.716990566

Reorder the terms:
-4.5 + x = -4.716990566

Solving
-4.5 + x = -4.716990566

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -4.716990566 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -4.716990566 + 4.5
x = -4.716990566 + 4.5

Combine like terms: -4.716990566 + 4.5 = -0.216990566
x = -0.216990566

Simplifying
x = -0.216990566

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.216990566, -0.216990566}
Solution
x = {9.216990566, -0.216990566}