5x-4x(x+8)=10x+24

Solution for 5x-4x(x+8)=10x+24 equation:

Simplifying
5x + -4x(x + 8) = 10x + 24

Reorder the terms:
5x + -4x(8 + x) = 10x + 24
5x + (8 * -4x + x * -4x) = 10x + 24
5x + (-32x + -4x2) = 10x + 24

Combine like terms: 5x + -32x = -27x
-27x + -4x2 = 10x + 24

Reorder the terms:
-27x + -4x2 = 24 + 10x

Solving
-27x + -4x2 = 24 + 10x

Solving for variable 'x'.

Reorder the terms:
-24 + -27x + -10x + -4x2 = 24 + 10x + -24 + -10x

Combine like terms: -27x + -10x = -37x
-24 + -37x + -4x2 = 24 + 10x + -24 + -10x

Reorder the terms:
-24 + -37x + -4x2 = 24 + -24 + 10x + -10x

Combine like terms: 24 + -24 = 0
-24 + -37x + -4x2 = 0 + 10x + -10x
-24 + -37x + -4x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-24 + -37x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(24 + 37x + 4x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(24 + 37x + 4x2)' equal to zero and attempt to solve:

Simplifying
24 + 37x + 4x2 = 0

Solving
24 + 37x + 4x2 = 0

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

Divide each side by '4'.
6 + 9.25x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 9.25x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 9.25x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 9.25x + x2 = 0 + -6
9.25x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
9.25x + x2 = -6

The x term is 9.25x.  Take half its coefficient (4.625).
Square it (21.390625) and add it to both sides.

Add '21.390625' to each side of the equation.
9.25x + 21.390625 + x2 = -6 + 21.390625

Reorder the terms:
21.390625 + 9.25x + x2 = -6 + 21.390625

Combine like terms: -6 + 21.390625 = 15.390625
21.390625 + 9.25x + x2 = 15.390625

Factor a perfect square on the left side:
(x + 4.625)(x + 4.625) = 15.390625

Calculate the square root of the right side: 3.923088707

Break this problem into two subproblems by setting 
(x + 4.625) equal to 3.923088707 and -3.923088707.

Subproblem 1
x + 4.625 = 3.923088707

Simplifying
x + 4.625 = 3.923088707

Reorder the terms:
4.625 + x = 3.923088707

Solving
4.625 + x = 3.923088707

Solving for variable 'x'.

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

Add '-4.625' to each side of the equation.
4.625 + -4.625 + x = 3.923088707 + -4.625

Combine like terms: 4.625 + -4.625 = 0.000
0.000 + x = 3.923088707 + -4.625
x = 3.923088707 + -4.625

Combine like terms: 3.923088707 + -4.625 = -0.701911293
x = -0.701911293

Simplifying
x = -0.701911293

Subproblem 2
x + 4.625 = -3.923088707

Simplifying
x + 4.625 = -3.923088707

Reorder the terms:
4.625 + x = -3.923088707

Solving
4.625 + x = -3.923088707

Solving for variable 'x'.

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

Add '-4.625' to each side of the equation.
4.625 + -4.625 + x = -3.923088707 + -4.625

Combine like terms: 4.625 + -4.625 = 0.000
0.000 + x = -3.923088707 + -4.625
x = -3.923088707 + -4.625

Combine like terms: -3.923088707 + -4.625 = -8.548088707
x = -8.548088707

Simplifying
x = -8.548088707

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.701911293, -8.548088707}
Solution
x = {-0.701911293, -8.548088707}