(3+h)(3+h)(3+h)-27=

Solution for (3+h)(3+h)(3+h)-27= equation:

Simplifying
(3 + h)(3 + h)(3 + h) + -27 = 0

Multiply (3 + h) * (3 + h)
(3(3 + h) + h(3 + h))(3 + h) + -27 = 0
((3 * 3 + h * 3) + h(3 + h))(3 + h) + -27 = 0
((9 + 3h) + h(3 + h))(3 + h) + -27 = 0
(9 + 3h + (3 * h + h * h))(3 + h) + -27 = 0
(9 + 3h + (3h + h2))(3 + h) + -27 = 0

Combine like terms: 3h + 3h = 6h
(9 + 6h + h2)(3 + h) + -27 = 0

Multiply (9 + 6h + h2) * (3 + h)
(9(3 + h) + 6h * (3 + h) + h2(3 + h)) + -27 = 0
((3 * 9 + h * 9) + 6h * (3 + h) + h2(3 + h)) + -27 = 0
((27 + 9h) + 6h * (3 + h) + h2(3 + h)) + -27 = 0
(27 + 9h + (3 * 6h + h * 6h) + h2(3 + h)) + -27 = 0
(27 + 9h + (18h + 6h2) + h2(3 + h)) + -27 = 0
(27 + 9h + 18h + 6h2 + (3 * h2 + h * h2)) + -27 = 0
(27 + 9h + 18h + 6h2 + (3h2 + h3)) + -27 = 0

Combine like terms: 9h + 18h = 27h
(27 + 27h + 6h2 + 3h2 + h3) + -27 = 0

Combine like terms: 6h2 + 3h2 = 9h2
(27 + 27h + 9h2 + h3) + -27 = 0

Reorder the terms:
27 + -27 + 27h + 9h2 + h3 = 0

Combine like terms: 27 + -27 = 0
0 + 27h + 9h2 + h3 = 0
27h + 9h2 + h3 = 0

Solving
27h + 9h2 + h3 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), 'h'.
h(27 + 9h + h2) = 0

Subproblem 1
Set the factor 'h' equal to zero and attempt to solve:

Simplifying
h = 0

Solving
h = 0

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

Simplifying
h = 0
Subproblem 2
Set the factor '(27 + 9h + h2)' equal to zero and attempt to solve:

Simplifying
27 + 9h + h2 = 0

Solving
27 + 9h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + 9h + -27 + h2 = 0 + -27

Reorder the terms:
27 + -27 + 9h + h2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + 9h + h2 = 0 + -27
9h + h2 = 0 + -27

Combine like terms: 0 + -27 = -27
9h + h2 = -27

The h term is 9h.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9h + 20.25 + h2 = -27 + 20.25

Reorder the terms:
20.25 + 9h + h2 = -27 + 20.25

Combine like terms: -27 + 20.25 = -6.75
20.25 + 9h + h2 = -6.75

Factor a perfect square on the left side:
(h + 4.5)(h + 4.5) = -6.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
h = {0}