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

Solution for 288=(x+4)10(x-1)+4x equation:

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

Reorder the terms:
288 = (4 + x) * 10(x + -1) + 4x

Reorder the terms:
288 = (4 + x) * 10(-1 + x) + 4x

Reorder the terms for easier multiplication:
288 = 10(4 + x)(-1 + x) + 4x

Multiply (4 + x) * (-1 + x)
288 = 10(4(-1 + x) + x(-1 + x)) + 4x
288 = 10((-1 * 4 + x * 4) + x(-1 + x)) + 4x
288 = 10((-4 + 4x) + x(-1 + x)) + 4x
288 = 10(-4 + 4x + (-1 * x + x * x)) + 4x
288 = 10(-4 + 4x + (-1x + x2)) + 4x

Combine like terms: 4x + -1x = 3x
288 = 10(-4 + 3x + x2) + 4x
288 = (-4 * 10 + 3x * 10 + x2 * 10) + 4x
288 = (-40 + 30x + 10x2) + 4x

Reorder the terms:
288 = -40 + 30x + 4x + 10x2

Combine like terms: 30x + 4x = 34x
288 = -40 + 34x + 10x2

Solving
288 = -40 + 34x + 10x2

Solving for variable 'x'.

Combine like terms: 288 + 40 = 328
328 + -34x + -10x2 = -40 + 34x + 10x2 + 40 + -34x + -10x2

Reorder the terms:
328 + -34x + -10x2 = -40 + 40 + 34x + -34x + 10x2 + -10x2

Combine like terms: -40 + 40 = 0
328 + -34x + -10x2 = 0 + 34x + -34x + 10x2 + -10x2
328 + -34x + -10x2 = 34x + -34x + 10x2 + -10x2

Combine like terms: 34x + -34x = 0
328 + -34x + -10x2 = 0 + 10x2 + -10x2
328 + -34x + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
328 + -34x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(164 + -17x + -5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(164 + -17x + -5x2)' equal to zero and attempt to solve:

Simplifying
164 + -17x + -5x2 = 0

Solving
164 + -17x + -5x2 = 0

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

Divide each side by '-5'.
-32.8 + 3.4x + x2 = 0

Move the constant term to the right:

Add '32.8' to each side of the equation.
-32.8 + 3.4x + 32.8 + x2 = 0 + 32.8

Reorder the terms:
-32.8 + 32.8 + 3.4x + x2 = 0 + 32.8

Combine like terms: -32.8 + 32.8 = 0.0
0.0 + 3.4x + x2 = 0 + 32.8
3.4x + x2 = 0 + 32.8

Combine like terms: 0 + 32.8 = 32.8
3.4x + x2 = 32.8

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 = 32.8 + 2.89

Reorder the terms:
2.89 + 3.4x + x2 = 32.8 + 2.89

Combine like terms: 32.8 + 2.89 = 35.69
2.89 + 3.4x + x2 = 35.69

Factor a perfect square on the left side:
(x + 1.7)(x + 1.7) = 35.69

Calculate the square root of the right side: 5.974110812

Break this problem into two subproblems by setting 
(x + 1.7) equal to 5.974110812 and -5.974110812.

Subproblem 1
x + 1.7 = 5.974110812

Simplifying
x + 1.7 = 5.974110812

Reorder the terms:
1.7 + x = 5.974110812

Solving
1.7 + x = 5.974110812

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 = 5.974110812 + -1.7

Combine like terms: 1.7 + -1.7 = 0.0
0.0 + x = 5.974110812 + -1.7
x = 5.974110812 + -1.7

Combine like terms: 5.974110812 + -1.7 = 4.274110812
x = 4.274110812

Simplifying
x = 4.274110812

Subproblem 2
x + 1.7 = -5.974110812

Simplifying
x + 1.7 = -5.974110812

Reorder the terms:
1.7 + x = -5.974110812

Solving
1.7 + x = -5.974110812

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 = -5.974110812 + -1.7

Combine like terms: 1.7 + -1.7 = 0.0
0.0 + x = -5.974110812 + -1.7
x = -5.974110812 + -1.7

Combine like terms: -5.974110812 + -1.7 = -7.674110812
x = -7.674110812

Simplifying
x = -7.674110812

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.274110812, -7.674110812}
Solution
x = {4.274110812, -7.674110812}