4x-2x(x-5)=-3+4x+9

Solution for 4x-2x(x-5)=-3+4x+9 equation:

Simplifying
4x + -2x(x + -5) = -3 + 4x + 9

Reorder the terms:
4x + -2x(-5 + x) = -3 + 4x + 9
4x + (-5 * -2x + x * -2x) = -3 + 4x + 9
4x + (10x + -2x2) = -3 + 4x + 9

Combine like terms: 4x + 10x = 14x
14x + -2x2 = -3 + 4x + 9

Reorder the terms:
14x + -2x2 = -3 + 9 + 4x

Combine like terms: -3 + 9 = 6
14x + -2x2 = 6 + 4x

Solving
14x + -2x2 = 6 + 4x

Solving for variable 'x'.

Reorder the terms:
-6 + 14x + -4x + -2x2 = 6 + 4x + -6 + -4x

Combine like terms: 14x + -4x = 10x
-6 + 10x + -2x2 = 6 + 4x + -6 + -4x

Reorder the terms:
-6 + 10x + -2x2 = 6 + -6 + 4x + -4x

Combine like terms: 6 + -6 = 0
-6 + 10x + -2x2 = 0 + 4x + -4x
-6 + 10x + -2x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-6 + 10x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 5x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 5x + -1x2)' equal to zero and attempt to solve:

Simplifying
-3 + 5x + -1x2 = 0

Solving
-3 + 5x + -1x2 = 0

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

Divide each side by '-1'.
3 + -5x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -5x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -5x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x + x2 = 0 + -3
-5x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-5x + x2 = -3

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -3 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -3 + 6.25

Combine like terms: -3 + 6.25 = 3.25
6.25 + -5x + x2 = 3.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
x + -2.5 = 1.802775638

Simplifying
x + -2.5 = 1.802775638

Reorder the terms:
-2.5 + x = 1.802775638

Solving
-2.5 + x = 1.802775638

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 1.802775638 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 1.802775638 + 2.5
x = 1.802775638 + 2.5

Combine like terms: 1.802775638 + 2.5 = 4.302775638
x = 4.302775638

Simplifying
x = 4.302775638

Subproblem 2
x + -2.5 = -1.802775638

Simplifying
x + -2.5 = -1.802775638

Reorder the terms:
-2.5 + x = -1.802775638

Solving
-2.5 + x = -1.802775638

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -1.802775638 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -1.802775638 + 2.5
x = -1.802775638 + 2.5

Combine like terms: -1.802775638 + 2.5 = 0.697224362
x = 0.697224362

Simplifying
x = 0.697224362

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.302775638, 0.697224362}
Solution
x = {4.302775638, 0.697224362}