5x(4x-10)=2

Solution for 5x(4x-10)=2 equation:

Simplifying
5x(4x + -10) = 2

Reorder the terms:
5x(-10 + 4x) = 2
(-10 * 5x + 4x * 5x) = 2
(-50x + 20x2) = 2

Solving
-50x + 20x2 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + -50x + 20x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -50x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -25x + 10x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -25x + 10x2)' equal to zero and attempt to solve:

Simplifying
-1 + -25x + 10x2 = 0

Solving
-1 + -25x + 10x2 = 0

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

Divide each side by '10'.
-0.1 + -2.5x + x2 = 0.0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + -2.5x + 0.1 + x2 = 0.0 + 0.1

Reorder the terms:
-0.1 + 0.1 + -2.5x + x2 = 0.0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + -2.5x + x2 = 0.0 + 0.1
-2.5x + x2 = 0.0 + 0.1

Combine like terms: 0.0 + 0.1 = 0.1
-2.5x + x2 = 0.1

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 0.1 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 0.1 + 1.5625

Combine like terms: 0.1 + 1.5625 = 1.6625
1.5625 + -2.5x + x2 = 1.6625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 1.6625

Calculate the square root of the right side: 1.289379696

Break this problem into two subproblems by setting 
(x + -1.25) equal to 1.289379696 and -1.289379696.

Subproblem 1
x + -1.25 = 1.289379696

Simplifying
x + -1.25 = 1.289379696

Reorder the terms:
-1.25 + x = 1.289379696

Solving
-1.25 + x = 1.289379696

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 1.289379696 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 1.289379696 + 1.25
x = 1.289379696 + 1.25

Combine like terms: 1.289379696 + 1.25 = 2.539379696
x = 2.539379696

Simplifying
x = 2.539379696

Subproblem 2
x + -1.25 = -1.289379696

Simplifying
x + -1.25 = -1.289379696

Reorder the terms:
-1.25 + x = -1.289379696

Solving
-1.25 + x = -1.289379696

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -1.289379696 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -1.289379696 + 1.25
x = -1.289379696 + 1.25

Combine like terms: -1.289379696 + 1.25 = -0.039379696
x = -0.039379696

Simplifying
x = -0.039379696

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.539379696, -0.039379696}
Solution
x = {2.539379696, -0.039379696}