8x(8-5)-50=5x(x-7)

Solution for 8x(8-5)-50=5x(x-7) equation:

Simplifying
8x(8 + -5) + -50 = 5x(x + -7)

Combine like terms: 8 + -5 = 3
8x(3) + -50 = 5x(x + -7)

Reorder the terms for easier multiplication:
8 * 3x + -50 = 5x(x + -7)

Multiply 8 * 3
24x + -50 = 5x(x + -7)

Reorder the terms:
-50 + 24x = 5x(x + -7)

Reorder the terms:
-50 + 24x = 5x(-7 + x)
-50 + 24x = (-7 * 5x + x * 5x)
-50 + 24x = (-35x + 5x2)

Solving
-50 + 24x = -35x + 5x2

Solving for variable 'x'.

Combine like terms: 24x + 35x = 59x
-50 + 59x + -5x2 = -35x + 5x2 + 35x + -5x2

Reorder the terms:
-50 + 59x + -5x2 = -35x + 35x + 5x2 + -5x2

Combine like terms: -35x + 35x = 0
-50 + 59x + -5x2 = 0 + 5x2 + -5x2
-50 + 59x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-50 + 59x + -5x2 = 0

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

Divide each side by '-5'.
10 + -11.8x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -11.8x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -11.8x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -11.8x + x2 = 0 + -10
-11.8x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-11.8x + x2 = -10

The x term is -11.8x.  Take half its coefficient (-5.9).
Square it (34.81) and add it to both sides.

Add '34.81' to each side of the equation.
-11.8x + 34.81 + x2 = -10 + 34.81

Reorder the terms:
34.81 + -11.8x + x2 = -10 + 34.81

Combine like terms: -10 + 34.81 = 24.81
34.81 + -11.8x + x2 = 24.81

Factor a perfect square on the left side:
(x + -5.9)(x + -5.9) = 24.81

Calculate the square root of the right side: 4.980963762

Break this problem into two subproblems by setting 
(x + -5.9) equal to 4.980963762 and -4.980963762.

Subproblem 1
x + -5.9 = 4.980963762

Simplifying
x + -5.9 = 4.980963762

Reorder the terms:
-5.9 + x = 4.980963762

Solving
-5.9 + x = 4.980963762

Solving for variable 'x'.

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

Add '5.9' to each side of the equation.
-5.9 + 5.9 + x = 4.980963762 + 5.9

Combine like terms: -5.9 + 5.9 = 0.0
0.0 + x = 4.980963762 + 5.9
x = 4.980963762 + 5.9

Combine like terms: 4.980963762 + 5.9 = 10.880963762
x = 10.880963762

Simplifying
x = 10.880963762

Subproblem 2
x + -5.9 = -4.980963762

Simplifying
x + -5.9 = -4.980963762

Reorder the terms:
-5.9 + x = -4.980963762

Solving
-5.9 + x = -4.980963762

Solving for variable 'x'.

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

Add '5.9' to each side of the equation.
-5.9 + 5.9 + x = -4.980963762 + 5.9

Combine like terms: -5.9 + 5.9 = 0.0
0.0 + x = -4.980963762 + 5.9
x = -4.980963762 + 5.9

Combine like terms: -4.980963762 + 5.9 = 0.919036238
x = 0.919036238

Simplifying
x = 0.919036238

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.880963762, 0.919036238}