4h+2=2h(h-3)

Solution for 4h+2=2h(h-3) equation:

Simplifying
4h + 2 = 2h(h + -3)

Reorder the terms:
2 + 4h = 2h(h + -3)

Reorder the terms:
2 + 4h = 2h(-3 + h)
2 + 4h = (-3 * 2h + h * 2h)
2 + 4h = (-6h + 2h2)

Solving
2 + 4h = -6h + 2h2

Solving for variable 'h'.

Combine like terms: 4h + 6h = 10h
2 + 10h + -2h2 = -6h + 2h2 + 6h + -2h2

Reorder the terms:
2 + 10h + -2h2 = -6h + 6h + 2h2 + -2h2

Combine like terms: -6h + 6h = 0
2 + 10h + -2h2 = 0 + 2h2 + -2h2
2 + 10h + -2h2 = 2h2 + -2h2

Combine like terms: 2h2 + -2h2 = 0
2 + 10h + -2h2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 5h + -1h2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + 5h + -1h2)' equal to zero and attempt to solve:

Simplifying
1 + 5h + -1h2 = 0

Solving
1 + 5h + -1h2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + -5h + h2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -5h + 1 + h2 = 0 + 1

Reorder the terms:
-1 + 1 + -5h + h2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5h + h2 = 0 + 1
-5h + h2 = 0 + 1

Combine like terms: 0 + 1 = 1
-5h + h2 = 1

The h term is -5h.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5h + 6.25 + h2 = 1 + 6.25

Reorder the terms:
6.25 + -5h + h2 = 1 + 6.25

Combine like terms: 1 + 6.25 = 7.25
6.25 + -5h + h2 = 7.25

Factor a perfect square on the left side:
(h + -2.5)(h + -2.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(h + -2.5) equal to 2.692582404 and -2.692582404.

Subproblem 1
h + -2.5 = 2.692582404

Simplifying
h + -2.5 = 2.692582404

Reorder the terms:
-2.5 + h = 2.692582404

Solving
-2.5 + h = 2.692582404

Solving for variable 'h'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + h = 2.692582404 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + h = 2.692582404 + 2.5
h = 2.692582404 + 2.5

Combine like terms: 2.692582404 + 2.5 = 5.192582404
h = 5.192582404

Simplifying
h = 5.192582404

Subproblem 2
h + -2.5 = -2.692582404

Simplifying
h + -2.5 = -2.692582404

Reorder the terms:
-2.5 + h = -2.692582404

Solving
-2.5 + h = -2.692582404

Solving for variable 'h'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + h = -2.692582404 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + h = -2.692582404 + 2.5
h = -2.692582404 + 2.5

Combine like terms: -2.692582404 + 2.5 = -0.192582404
h = -0.192582404

Simplifying
h = -0.192582404

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {5.192582404, -0.192582404}
Solution
h = {5.192582404, -0.192582404}