4h^2+5h+1=0

Solution for 4h^2+5h+1=0 equation:

Simplifying
4h2 + 5h + 1 = 0

Reorder the terms:
1 + 5h + 4h2 = 0

Solving
1 + 5h + 4h2 = 0

Solving for variable 'h'.

Factor a trinomial.
(1 + h)(1 + 4h) = 0

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

Simplifying
1 + h = 0

Solving
1 + h = 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 + h = 0 + -1

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

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

Simplifying
h = -1
Subproblem 2
Set the factor '(1 + 4h)' equal to zero and attempt to solve:

Simplifying
1 + 4h = 0

Solving
1 + 4h = 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 + 4h = 0 + -1

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

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

Divide each side by '4'.
h = -0.25

Simplifying
h = -0.25
Solution
h = {-1, -0.25}