4x+(x+4)10(x-1)=24

Solution for 4x+(x+4)10(x-1)=24 equation:

Simplifying
4x + (x + 4) * 10(x + -1) = 24

Reorder the terms:
4x + (4 + x) * 10(x + -1) = 24

Reorder the terms:
4x + (4 + x) * 10(-1 + x) = 24

Reorder the terms for easier multiplication:
4x + 10(4 + x)(-1 + x) = 24

Multiply (4 + x) * (-1 + x)
4x + 10(4(-1 + x) + x(-1 + x)) = 24
4x + 10((-1 * 4 + x * 4) + x(-1 + x)) = 24
4x + 10((-4 + 4x) + x(-1 + x)) = 24
4x + 10(-4 + 4x + (-1 * x + x * x)) = 24
4x + 10(-4 + 4x + (-1x + x2)) = 24

Combine like terms: 4x + -1x = 3x
4x + 10(-4 + 3x + x2) = 24
4x + (-4 * 10 + 3x * 10 + x2 * 10) = 24
4x + (-40 + 30x + 10x2) = 24

Reorder the terms:
-40 + 4x + 30x + 10x2 = 24

Combine like terms: 4x + 30x = 34x
-40 + 34x + 10x2 = 24

Solving
-40 + 34x + 10x2 = 24

Solving for variable 'x'.

Reorder the terms:
-40 + -24 + 34x + 10x2 = 24 + -24

Combine like terms: -40 + -24 = -64
-64 + 34x + 10x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-64 + 34x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-32 + 17x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-32 + 17x + 5x2)' equal to zero and attempt to solve:

Simplifying
-32 + 17x + 5x2 = 0

Solving
-32 + 17x + 5x2 = 0

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

Divide each side by '5'.
-6.4 + 3.4x + x2 = 0

Move the constant term to the right:

Add '6.4' to each side of the equation.
-6.4 + 3.4x + 6.4 + x2 = 0 + 6.4

Reorder the terms:
-6.4 + 6.4 + 3.4x + x2 = 0 + 6.4

Combine like terms: -6.4 + 6.4 = 0.0
0.0 + 3.4x + x2 = 0 + 6.4
3.4x + x2 = 0 + 6.4

Combine like terms: 0 + 6.4 = 6.4
3.4x + x2 = 6.4

The x term is 3.4x.  Take half its coefficient (1.7).
Square it (2.89) and add it to both sides.

Add '2.89' to each side of the equation.
3.4x + 2.89 + x2 = 6.4 + 2.89

Reorder the terms:
2.89 + 3.4x + x2 = 6.4 + 2.89

Combine like terms: 6.4 + 2.89 = 9.29
2.89 + 3.4x + x2 = 9.29

Factor a perfect square on the left side:
(x + 1.7)(x + 1.7) = 9.29

Calculate the square root of the right side: 3.047950131

Break this problem into two subproblems by setting 
(x + 1.7) equal to 3.047950131 and -3.047950131.

Subproblem 1
x + 1.7 = 3.047950131

Simplifying
x + 1.7 = 3.047950131

Reorder the terms:
1.7 + x = 3.047950131

Solving
1.7 + x = 3.047950131

Solving for variable 'x'.

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

Add '-1.7' to each side of the equation.
1.7 + -1.7 + x = 3.047950131 + -1.7

Combine like terms: 1.7 + -1.7 = 0.0
0.0 + x = 3.047950131 + -1.7
x = 3.047950131 + -1.7

Combine like terms: 3.047950131 + -1.7 = 1.347950131
x = 1.347950131

Simplifying
x = 1.347950131

Subproblem 2
x + 1.7 = -3.047950131

Simplifying
x + 1.7 = -3.047950131

Reorder the terms:
1.7 + x = -3.047950131

Solving
1.7 + x = -3.047950131

Solving for variable 'x'.

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

Add '-1.7' to each side of the equation.
1.7 + -1.7 + x = -3.047950131 + -1.7

Combine like terms: 1.7 + -1.7 = 0.0
0.0 + x = -3.047950131 + -1.7
x = -3.047950131 + -1.7

Combine like terms: -3.047950131 + -1.7 = -4.747950131
x = -4.747950131

Simplifying
x = -4.747950131

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.347950131, -4.747950131}
Solution
x = {1.347950131, -4.747950131}