h(h-3)+1=4h-1

Solution for h(h-3)+1=4h-1 equation:

Simplifying
h(h + -3) + 1 = 4h + -1

Reorder the terms:
h(-3 + h) + 1 = 4h + -1
(-3 * h + h * h) + 1 = 4h + -1
(-3h + h2) + 1 = 4h + -1

Reorder the terms:
1 + -3h + h2 = 4h + -1

Reorder the terms:
1 + -3h + h2 = -1 + 4h

Solving
1 + -3h + h2 = -1 + 4h

Solving for variable 'h'.

Reorder the terms:
1 + 1 + -3h + -4h + h2 = -1 + 4h + 1 + -4h

Combine like terms: 1 + 1 = 2
2 + -3h + -4h + h2 = -1 + 4h + 1 + -4h

Combine like terms: -3h + -4h = -7h
2 + -7h + h2 = -1 + 4h + 1 + -4h

Reorder the terms:
2 + -7h + h2 = -1 + 1 + 4h + -4h

Combine like terms: -1 + 1 = 0
2 + -7h + h2 = 0 + 4h + -4h
2 + -7h + h2 = 4h + -4h

Combine like terms: 4h + -4h = 0
2 + -7h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -7h + -2 + h2 = 0 + -2

Reorder the terms:
2 + -2 + -7h + h2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7h + h2 = 0 + -2
-7h + h2 = 0 + -2

Combine like terms: 0 + -2 = -2
-7h + h2 = -2

The h term is -7h.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7h + 12.25 + h2 = -2 + 12.25

Reorder the terms:
12.25 + -7h + h2 = -2 + 12.25

Combine like terms: -2 + 12.25 = 10.25
12.25 + -7h + h2 = 10.25

Factor a perfect square on the left side:
(h + -3.5)(h + -3.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(h + -3.5) equal to 3.201562119 and -3.201562119.

Subproblem 1
h + -3.5 = 3.201562119

Simplifying
h + -3.5 = 3.201562119

Reorder the terms:
-3.5 + h = 3.201562119

Solving
-3.5 + h = 3.201562119

Solving for variable 'h'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + h = 3.201562119 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + h = 3.201562119 + 3.5
h = 3.201562119 + 3.5

Combine like terms: 3.201562119 + 3.5 = 6.701562119
h = 6.701562119

Simplifying
h = 6.701562119

Subproblem 2
h + -3.5 = -3.201562119

Simplifying
h + -3.5 = -3.201562119

Reorder the terms:
-3.5 + h = -3.201562119

Solving
-3.5 + h = -3.201562119

Solving for variable 'h'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + h = -3.201562119 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + h = -3.201562119 + 3.5
h = -3.201562119 + 3.5

Combine like terms: -3.201562119 + 3.5 = 0.298437881
h = 0.298437881

Simplifying
h = 0.298437881

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {6.701562119, 0.298437881}