3h^2+4h=55

Solution for 3h^2+4h=55 equation:

Simplifying
3h2 + 4h = 55

Reorder the terms:
4h + 3h2 = 55

Solving
4h + 3h2 = 55

Solving for variable 'h'.

Reorder the terms:
-55 + 4h + 3h2 = 55 + -55

Combine like terms: 55 + -55 = 0
-55 + 4h + 3h2 = 0

Factor a trinomial.
(-5 + -1h)(11 + -3h) = 0

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

Simplifying
-5 + -1h = 0

Solving
-5 + -1h = 0

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

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

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

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

Divide each side by '-1'.
h = -5

Simplifying
h = -5
Subproblem 2
Set the factor '(11 + -3h)' equal to zero and attempt to solve:

Simplifying
11 + -3h = 0

Solving
11 + -3h = 0

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

Add '-11' to each side of the equation.
11 + -11 + -3h = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3h = 0 + -11
-3h = 0 + -11

Combine like terms: 0 + -11 = -11
-3h = -11

Divide each side by '-3'.
h = 3.666666667

Simplifying
h = 3.666666667
Solution
h = {-5, 3.666666667}