2(h+3)5h=-3

Solution for 2(h+3)5h=-3 equation:

Simplifying
2(h + 3) * 5h = -3

Reorder the terms:
2(3 + h) * 5h = -3

Reorder the terms for easier multiplication:
2 * 5h(3 + h) = -3

Multiply 2 * 5
10h(3 + h) = -3
(3 * 10h + h * 10h) = -3
(30h + 10h2) = -3

Solving
30h + 10h2 = -3

Solving for variable 'h'.

Reorder the terms:
3 + 30h + 10h2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + 30h + 10h2 = 0

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

Divide each side by '10'.
0.3 + 3h + h2 = 0.0

Move the constant term to the right:

Add '-0.3' to each side of the equation.
0.3 + 3h + -0.3 + h2 = 0.0 + -0.3

Reorder the terms:
0.3 + -0.3 + 3h + h2 = 0.0 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + 3h + h2 = 0.0 + -0.3
3h + h2 = 0.0 + -0.3

Combine like terms: 0.0 + -0.3 = -0.3
3h + h2 = -0.3

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 = -0.3 + 2.25

Reorder the terms:
2.25 + 3h + h2 = -0.3 + 2.25

Combine like terms: -0.3 + 2.25 = 1.95
2.25 + 3h + h2 = 1.95

Factor a perfect square on the left side:
(h + 1.5)(h + 1.5) = 1.95

Calculate the square root of the right side: 1.396424004

Break this problem into two subproblems by setting 
(h + 1.5) equal to 1.396424004 and -1.396424004.

Subproblem 1
h + 1.5 = 1.396424004

Simplifying
h + 1.5 = 1.396424004

Reorder the terms:
1.5 + h = 1.396424004

Solving
1.5 + h = 1.396424004

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 = 1.396424004 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + h = 1.396424004 + -1.5
h = 1.396424004 + -1.5

Combine like terms: 1.396424004 + -1.5 = -0.103575996
h = -0.103575996

Simplifying
h = -0.103575996

Subproblem 2
h + 1.5 = -1.396424004

Simplifying
h + 1.5 = -1.396424004

Reorder the terms:
1.5 + h = -1.396424004

Solving
1.5 + h = -1.396424004

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 = -1.396424004 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + h = -1.396424004 + -1.5
h = -1.396424004 + -1.5

Combine like terms: -1.396424004 + -1.5 = -2.896424004
h = -2.896424004

Simplifying
h = -2.896424004

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {-0.103575996, -2.896424004}