8(659464-7649x)=649x(8x+64x)

Solution for 8(659464-7649x)=649x(8x+64x) equation:

Simplifying
8(659464 + -7649x) = 649x(8x + 64x)
(659464 * 8 + -7649x * 8) = 649x(8x + 64x)
(5275712 + -61192x) = 649x(8x + 64x)

Combine like terms: 8x + 64x = 72x
5275712 + -61192x = 649x(72x)

Remove parenthesis around (72x)
5275712 + -61192x = 649x * 72x

Reorder the terms for easier multiplication:
5275712 + -61192x = 649 * 72x * x

Multiply 649 * 72
5275712 + -61192x = 46728x * x

Multiply x * x
5275712 + -61192x = 46728x2

Solving
5275712 + -61192x = 46728x2

Solving for variable 'x'.

Combine like terms: 46728x2 + -46728x2 = 0
5275712 + -61192x + -46728x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(659464 + -7649x + -5841x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(659464 + -7649x + -5841x2)' equal to zero and attempt to solve:

Simplifying
659464 + -7649x + -5841x2 = 0

Solving
659464 + -7649x + -5841x2 = 0

Begin completing the square.  Divide all terms by
-5841 the coefficient of the squared term: 

Divide each side by '-5841'.
-112.9025852 + 1.309536038x + x2 = 0

Move the constant term to the right:

Add '112.9025852' to each side of the equation.
-112.9025852 + 1.309536038x + 112.9025852 + x2 = 0 + 112.9025852

Reorder the terms:
-112.9025852 + 112.9025852 + 1.309536038x + x2 = 0 + 112.9025852

Combine like terms: -112.9025852 + 112.9025852 = 0.0000000
0.0000000 + 1.309536038x + x2 = 0 + 112.9025852
1.309536038x + x2 = 0 + 112.9025852

Combine like terms: 0 + 112.9025852 = 112.9025852
1.309536038x + x2 = 112.9025852

The x term is 1.309536038x.  Take half its coefficient (0.654768019).
Square it (0.4287211587) and add it to both sides.

Add '0.4287211587' to each side of the equation.
1.309536038x + 0.4287211587 + x2 = 112.9025852 + 0.4287211587

Reorder the terms:
0.4287211587 + 1.309536038x + x2 = 112.9025852 + 0.4287211587

Combine like terms: 112.9025852 + 0.4287211587 = 113.3313063587
0.4287211587 + 1.309536038x + x2 = 113.3313063587

Factor a perfect square on the left side:
(x + 0.654768019)(x + 0.654768019) = 113.3313063587

Calculate the square root of the right side: 10.645717747

Break this problem into two subproblems by setting 
(x + 0.654768019) equal to 10.645717747 and -10.645717747.

Subproblem 1
x + 0.654768019 = 10.645717747

Simplifying
x + 0.654768019 = 10.645717747

Reorder the terms:
0.654768019 + x = 10.645717747

Solving
0.654768019 + x = 10.645717747

Solving for variable 'x'.

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

Add '-0.654768019' to each side of the equation.
0.654768019 + -0.654768019 + x = 10.645717747 + -0.654768019

Combine like terms: 0.654768019 + -0.654768019 = 0.000000000
0.000000000 + x = 10.645717747 + -0.654768019
x = 10.645717747 + -0.654768019

Combine like terms: 10.645717747 + -0.654768019 = 9.990949728
x = 9.990949728

Simplifying
x = 9.990949728

Subproblem 2
x + 0.654768019 = -10.645717747

Simplifying
x + 0.654768019 = -10.645717747

Reorder the terms:
0.654768019 + x = -10.645717747

Solving
0.654768019 + x = -10.645717747

Solving for variable 'x'.

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

Add '-0.654768019' to each side of the equation.
0.654768019 + -0.654768019 + x = -10.645717747 + -0.654768019

Combine like terms: 0.654768019 + -0.654768019 = 0.000000000
0.000000000 + x = -10.645717747 + -0.654768019
x = -10.645717747 + -0.654768019

Combine like terms: -10.645717747 + -0.654768019 = -11.300485766
x = -11.300485766

Simplifying
x = -11.300485766

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.990949728, -11.300485766}
Solution
x = {9.990949728, -11.300485766}