(3+h)(h)=27

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

Simplifying
(3 + h)(h) = 27

Reorder the terms for easier multiplication:
h(3 + h) = 27
(3 * h + h * h) = 27
(3h + h2) = 27

Solving
3h + h2 = 27

Solving for variable 'h'.

Reorder the terms:
-27 + 3h + h2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + 3h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + 3h + 27 + h2 = 0 + 27

Reorder the terms:
-27 + 27 + 3h + h2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 3h + h2 = 0 + 27
3h + h2 = 0 + 27

Combine like terms: 0 + 27 = 27
3h + h2 = 27

The h term is 3h.  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.
3h + 2.25 + h2 = 27 + 2.25

Reorder the terms:
2.25 + 3h + h2 = 27 + 2.25

Combine like terms: 27 + 2.25 = 29.25
2.25 + 3h + h2 = 29.25

Factor a perfect square on the left side:
(h + 1.5)(h + 1.5) = 29.25

Calculate the square root of the right side: 5.408326913

Break this problem into two subproblems by setting 
(h + 1.5) equal to 5.408326913 and -5.408326913.

Subproblem 1
h + 1.5 = 5.408326913

Simplifying
h + 1.5 = 5.408326913

Reorder the terms:
1.5 + h = 5.408326913

Solving
1.5 + h = 5.408326913

Solving for variable 'h'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + h = 5.408326913 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + h = 5.408326913 + -1.5
h = 5.408326913 + -1.5

Combine like terms: 5.408326913 + -1.5 = 3.908326913
h = 3.908326913

Simplifying
h = 3.908326913

Subproblem 2
h + 1.5 = -5.408326913

Simplifying
h + 1.5 = -5.408326913

Reorder the terms:
1.5 + h = -5.408326913

Solving
1.5 + h = -5.408326913

Solving for variable 'h'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + h = -5.408326913 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + h = -5.408326913 + -1.5
h = -5.408326913 + -1.5

Combine like terms: -5.408326913 + -1.5 = -6.908326913
h = -6.908326913

Simplifying
h = -6.908326913

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {3.908326913, -6.908326913}