4(x-5)2x-1+3=

Solution for 4(x-5)2x-1+3= equation:

Simplifying
4(x + -5) * 2x + -1 + 3 = 0

Reorder the terms:
4(-5 + x) * 2x + -1 + 3 = 0

Reorder the terms for easier multiplication:
4 * 2x(-5 + x) + -1 + 3 = 0

Multiply 4 * 2
8x(-5 + x) + -1 + 3 = 0
(-5 * 8x + x * 8x) + -1 + 3 = 0
(-40x + 8x2) + -1 + 3 = 0

Reorder the terms:
-1 + 3 + -40x + 8x2 = 0

Combine like terms: -1 + 3 = 2
2 + -40x + 8x2 = 0

Solving
2 + -40x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -20x + 4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -20x + 4x2)' equal to zero and attempt to solve:

Simplifying
1 + -20x + 4x2 = 0

Solving
1 + -20x + 4x2 = 0

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

Divide each side by '4'.
0.25 + -5x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -5x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -5x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -5x + x2 = 0 + -0.25
-5x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-5x + x2 = -0.25

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 = -0.25 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -0.25 + 6.25

Combine like terms: -0.25 + 6.25 = 6
6.25 + -5x + x2 = 6

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.449489743 and -2.449489743.

Subproblem 1
x + -2.5 = 2.449489743

Simplifying
x + -2.5 = 2.449489743

Reorder the terms:
-2.5 + x = 2.449489743

Solving
-2.5 + x = 2.449489743

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 = 2.449489743 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.449489743 + 2.5
x = 2.449489743 + 2.5

Combine like terms: 2.449489743 + 2.5 = 4.949489743
x = 4.949489743

Simplifying
x = 4.949489743

Subproblem 2
x + -2.5 = -2.449489743

Simplifying
x + -2.5 = -2.449489743

Reorder the terms:
-2.5 + x = -2.449489743

Solving
-2.5 + x = -2.449489743

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 = -2.449489743 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.449489743 + 2.5
x = -2.449489743 + 2.5

Combine like terms: -2.449489743 + 2.5 = 0.050510257
x = 0.050510257

Simplifying
x = 0.050510257

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.949489743, 0.050510257}
Solution
x = {4.949489743, 0.050510257}