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

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

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

Reorder the terms:
2x(-4 + 5x) = 4(-1x + 1)
(-4 * 2x + 5x * 2x) = 4(-1x + 1)
(-8x + 10x2) = 4(-1x + 1)

Reorder the terms:
-8x + 10x2 = 4(1 + -1x)
-8x + 10x2 = (1 * 4 + -1x * 4)
-8x + 10x2 = (4 + -4x)

Solving
-8x + 10x2 = 4 + -4x

Solving for variable 'x'.

Reorder the terms:
-4 + -8x + 4x + 10x2 = 4 + -4x + -4 + 4x

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

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

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

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

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

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

Simplifying
-2 + -2x + 5x2 = 0

Solving
-2 + -2x + 5x2 = 0

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

Divide each side by '5'.
-0.4 + -0.4x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -0.4x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -0.4x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -0.4x + x2 = 0 + 0.4
-0.4x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
-0.4x + x2 = 0.4

The x term is -0.4x.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4x + 0.04 + x2 = 0.4 + 0.04

Reorder the terms:
0.04 + -0.4x + x2 = 0.4 + 0.04

Combine like terms: 0.4 + 0.04 = 0.44
0.04 + -0.4x + x2 = 0.44

Factor a perfect square on the left side:
(x + -0.2)(x + -0.2) = 0.44

Calculate the square root of the right side: 0.663324958

Break this problem into two subproblems by setting 
(x + -0.2) equal to 0.663324958 and -0.663324958.

Subproblem 1
x + -0.2 = 0.663324958

Simplifying
x + -0.2 = 0.663324958

Reorder the terms:
-0.2 + x = 0.663324958

Solving
-0.2 + x = 0.663324958

Solving for variable 'x'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + x = 0.663324958 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + x = 0.663324958 + 0.2
x = 0.663324958 + 0.2

Combine like terms: 0.663324958 + 0.2 = 0.863324958
x = 0.863324958

Simplifying
x = 0.863324958

Subproblem 2
x + -0.2 = -0.663324958

Simplifying
x + -0.2 = -0.663324958

Reorder the terms:
-0.2 + x = -0.663324958

Solving
-0.2 + x = -0.663324958

Solving for variable 'x'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + x = -0.663324958 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + x = -0.663324958 + 0.2
x = -0.663324958 + 0.2

Combine like terms: -0.663324958 + 0.2 = -0.463324958
x = -0.463324958

Simplifying
x = -0.463324958

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.863324958, -0.463324958}
Solution
x = {0.863324958, -0.463324958}