-7x+8(-5x+3)=x(2x-7)

Solution for -7x+8(-5x+3)=x(2x-7) equation:

Simplifying
-7x + 8(-5x + 3) = x(2x + -7)

Reorder the terms:
-7x + 8(3 + -5x) = x(2x + -7)
-7x + (3 * 8 + -5x * 8) = x(2x + -7)
-7x + (24 + -40x) = x(2x + -7)

Reorder the terms:
24 + -7x + -40x = x(2x + -7)

Combine like terms: -7x + -40x = -47x
24 + -47x = x(2x + -7)

Reorder the terms:
24 + -47x = x(-7 + 2x)
24 + -47x = (-7 * x + 2x * x)
24 + -47x = (-7x + 2x2)

Solving
24 + -47x = -7x + 2x2

Solving for variable 'x'.

Combine like terms: -47x + 7x = -40x
24 + -40x + -2x2 = -7x + 2x2 + 7x + -2x2

Reorder the terms:
24 + -40x + -2x2 = -7x + 7x + 2x2 + -2x2

Combine like terms: -7x + 7x = 0
24 + -40x + -2x2 = 0 + 2x2 + -2x2
24 + -40x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
24 + -40x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -20x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(12 + -20x + -1x2)' equal to zero and attempt to solve:

Simplifying
12 + -20x + -1x2 = 0

Solving
12 + -20x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-12 + 20x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 20x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 20x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 20x + x2 = 0 + 12
20x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
20x + x2 = 12

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 12 + 100

Reorder the terms:
100 + 20x + x2 = 12 + 100

Combine like terms: 12 + 100 = 112
100 + 20x + x2 = 112

Factor a perfect square on the left side:
(x + 10)(x + 10) = 112

Calculate the square root of the right side: 10.583005244

Break this problem into two subproblems by setting 
(x + 10) equal to 10.583005244 and -10.583005244.

Subproblem 1
x + 10 = 10.583005244

Simplifying
x + 10 = 10.583005244

Reorder the terms:
10 + x = 10.583005244

Solving
10 + x = 10.583005244

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 10.583005244 + -10

Combine like terms: 10 + -10 = 0
0 + x = 10.583005244 + -10
x = 10.583005244 + -10

Combine like terms: 10.583005244 + -10 = 0.583005244
x = 0.583005244

Simplifying
x = 0.583005244

Subproblem 2
x + 10 = -10.583005244

Simplifying
x + 10 = -10.583005244

Reorder the terms:
10 + x = -10.583005244

Solving
10 + x = -10.583005244

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -10.583005244 + -10

Combine like terms: 10 + -10 = 0
0 + x = -10.583005244 + -10
x = -10.583005244 + -10

Combine like terms: -10.583005244 + -10 = -20.583005244
x = -20.583005244

Simplifying
x = -20.583005244

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.583005244, -20.583005244}
Solution
x = {0.583005244, -20.583005244}