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

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

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

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

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

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

Multiply 4 * 10
288 = 40(4 + x)(-1 + x)

Multiply (4 + x) * (-1 + x)
288 = 40(4(-1 + x) + x(-1 + x))
288 = 40((-1 * 4 + x * 4) + x(-1 + x))
288 = 40((-4 + 4x) + x(-1 + x))
288 = 40(-4 + 4x + (-1 * x + x * x))
288 = 40(-4 + 4x + (-1x + x2))

Combine like terms: 4x + -1x = 3x
288 = 40(-4 + 3x + x2)
288 = (-4 * 40 + 3x * 40 + x2 * 40)
288 = (-160 + 120x + 40x2)

Solving
288 = -160 + 120x + 40x2

Solving for variable 'x'.

Combine like terms: 288 + 160 = 448
448 + -120x + -40x2 = -160 + 120x + 40x2 + 160 + -120x + -40x2

Reorder the terms:
448 + -120x + -40x2 = -160 + 160 + 120x + -120x + 40x2 + -40x2

Combine like terms: -160 + 160 = 0
448 + -120x + -40x2 = 0 + 120x + -120x + 40x2 + -40x2
448 + -120x + -40x2 = 120x + -120x + 40x2 + -40x2

Combine like terms: 120x + -120x = 0
448 + -120x + -40x2 = 0 + 40x2 + -40x2
448 + -120x + -40x2 = 40x2 + -40x2

Combine like terms: 40x2 + -40x2 = 0
448 + -120x + -40x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(56 + -15x + -5x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(56 + -15x + -5x2)' equal to zero and attempt to solve:

Simplifying
56 + -15x + -5x2 = 0

Solving
56 + -15x + -5x2 = 0

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

Divide each side by '-5'.
-11.2 + 3x + x2 = 0

Move the constant term to the right:

Add '11.2' to each side of the equation.
-11.2 + 3x + 11.2 + x2 = 0 + 11.2

Reorder the terms:
-11.2 + 11.2 + 3x + x2 = 0 + 11.2

Combine like terms: -11.2 + 11.2 = 0.0
0.0 + 3x + x2 = 0 + 11.2
3x + x2 = 0 + 11.2

Combine like terms: 0 + 11.2 = 11.2
3x + x2 = 11.2

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 11.2 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 11.2 + 2.25

Combine like terms: 11.2 + 2.25 = 13.45
2.25 + 3x + x2 = 13.45

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 13.45

Calculate the square root of the right side: 3.667424164

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.667424164 and -3.667424164.

Subproblem 1
x + 1.5 = 3.667424164

Simplifying
x + 1.5 = 3.667424164

Reorder the terms:
1.5 + x = 3.667424164

Solving
1.5 + x = 3.667424164

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 3.667424164 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 3.667424164 + -1.5
x = 3.667424164 + -1.5

Combine like terms: 3.667424164 + -1.5 = 2.167424164
x = 2.167424164

Simplifying
x = 2.167424164

Subproblem 2
x + 1.5 = -3.667424164

Simplifying
x + 1.5 = -3.667424164

Reorder the terms:
1.5 + x = -3.667424164

Solving
1.5 + x = -3.667424164

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -3.667424164 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -3.667424164 + -1.5
x = -3.667424164 + -1.5

Combine like terms: -3.667424164 + -1.5 = -5.167424164
x = -5.167424164

Simplifying
x = -5.167424164

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.167424164, -5.167424164}
Solution
x = {2.167424164, -5.167424164}