30(2)=(3+2h)h

Solution for 30(2)=(3+2h)h equation:

Simplifying
30(2) = (3 + 2h) * h

Multiply 30 * 2
60 = (3 + 2h) * h

Reorder the terms for easier multiplication:
60 = h(3 + 2h)
60 = (3 * h + 2h * h)
60 = (3h + 2h2)

Solving
60 = 3h + 2h2

Solving for variable 'h'.

Reorder the terms:
60 + -3h + -2h2 = 3h + -3h + 2h2 + -2h2

Combine like terms: 3h + -3h = 0
60 + -3h + -2h2 = 0 + 2h2 + -2h2
60 + -3h + -2h2 = 2h2 + -2h2

Combine like terms: 2h2 + -2h2 = 0
60 + -3h + -2h2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-30 + 1.5h + h2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 1.5h + 30 + h2 = 0 + 30

Reorder the terms:
-30 + 30 + 1.5h + h2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 1.5h + h2 = 0 + 30
1.5h + h2 = 0 + 30

Combine like terms: 0 + 30 = 30
1.5h + h2 = 30

The h term is 1.5h.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5h + 0.5625 + h2 = 30 + 0.5625

Reorder the terms:
0.5625 + 1.5h + h2 = 30 + 0.5625

Combine like terms: 30 + 0.5625 = 30.5625
0.5625 + 1.5h + h2 = 30.5625

Factor a perfect square on the left side:
(h + 0.75)(h + 0.75) = 30.5625

Calculate the square root of the right side: 5.528336097

Break this problem into two subproblems by setting 
(h + 0.75) equal to 5.528336097 and -5.528336097.

Subproblem 1
h + 0.75 = 5.528336097

Simplifying
h + 0.75 = 5.528336097

Reorder the terms:
0.75 + h = 5.528336097

Solving
0.75 + h = 5.528336097

Solving for variable 'h'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + h = 5.528336097 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + h = 5.528336097 + -0.75
h = 5.528336097 + -0.75

Combine like terms: 5.528336097 + -0.75 = 4.778336097
h = 4.778336097

Simplifying
h = 4.778336097

Subproblem 2
h + 0.75 = -5.528336097

Simplifying
h + 0.75 = -5.528336097

Reorder the terms:
0.75 + h = -5.528336097

Solving
0.75 + h = -5.528336097

Solving for variable 'h'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + h = -5.528336097 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + h = -5.528336097 + -0.75
h = -5.528336097 + -0.75

Combine like terms: -5.528336097 + -0.75 = -6.278336097
h = -6.278336097

Simplifying
h = -6.278336097

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {4.778336097, -6.278336097}