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

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

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

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

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

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

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

Solving for variable 'h'.

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

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

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

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

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

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

Factor a trinomial.
(1 + -1h)(2 + h) = 0

Subproblem 1
Set the factor '(1 + -1h)' equal to zero and attempt to solve:

Simplifying
1 + -1h = 0

Solving
1 + -1h = 0

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

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

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

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

Divide each side by '-1'.
h = 1

Simplifying
h = 1
Subproblem 2
Set the factor '(2 + h)' equal to zero and attempt to solve:

Simplifying
2 + h = 0

Solving
2 + h = 0

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

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

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

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

Simplifying
h = -2
Solution
h = {1, -2}