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

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

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

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

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

Solving
-20x + 50x2 = 50 + 10x

Solving for variable 'x'.

Reorder the terms:
-50 + -20x + -10x + 50x2 = 50 + 10x + -50 + -10x

Combine like terms: -20x + -10x = -30x
-50 + -30x + 50x2 = 50 + 10x + -50 + -10x

Reorder the terms:
-50 + -30x + 50x2 = 50 + -50 + 10x + -10x

Combine like terms: 50 + -50 = 0
-50 + -30x + 50x2 = 0 + 10x + -10x
-50 + -30x + 50x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-50 + -30x + 50x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-5 + -3x + 5x2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-5 + -3x + 5x2)' equal to zero and attempt to solve:

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

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

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

Divide each side by '5'.
-1 + -0.6x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.6x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -0.6x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.6x + x2 = 0 + 1
-0.6x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.6x + x2 = 1

The x term is -0.6x.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6x + 0.09 + x2 = 1 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = 1 + 0.09

Combine like terms: 1 + 0.09 = 1.09
0.09 + -0.6x + x2 = 1.09

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = 1.09

Calculate the square root of the right side: 1.044030651

Break this problem into two subproblems by setting 
(x + -0.3) equal to 1.044030651 and -1.044030651.

Subproblem 1
x + -0.3 = 1.044030651

Simplifying
x + -0.3 = 1.044030651

Reorder the terms:
-0.3 + x = 1.044030651

Solving
-0.3 + x = 1.044030651

Solving for variable 'x'.

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

Add '0.3' to each side of the equation.
-0.3 + 0.3 + x = 1.044030651 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = 1.044030651 + 0.3
x = 1.044030651 + 0.3

Combine like terms: 1.044030651 + 0.3 = 1.344030651
x = 1.344030651

Simplifying
x = 1.344030651

Subproblem 2
x + -0.3 = -1.044030651

Simplifying
x + -0.3 = -1.044030651

Reorder the terms:
-0.3 + x = -1.044030651

Solving
-0.3 + x = -1.044030651

Solving for variable 'x'.

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

Add '0.3' to each side of the equation.
-0.3 + 0.3 + x = -1.044030651 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = -1.044030651 + 0.3
x = -1.044030651 + 0.3

Combine like terms: -1.044030651 + 0.3 = -0.744030651
x = -0.744030651

Simplifying
x = -0.744030651

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.344030651, -0.744030651}
Solution
x = {1.344030651, -0.744030651}