2h+3h+4h^2=84

Solution for 2h+3h+4h^2=84 equation:

Simplifying
2h + 3h + 4h2 = 84

Combine like terms: 2h + 3h = 5h
5h + 4h2 = 84

Solving
5h + 4h2 = 84

Solving for variable 'h'.

Reorder the terms:
-84 + 5h + 4h2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + 5h + 4h2 = 0

Factor a trinomial.
(-21 + -4h)(4 + -1h) = 0

Subproblem 1
Set the factor '(-21 + -4h)' equal to zero and attempt to solve:

Simplifying
-21 + -4h = 0

Solving
-21 + -4h = 0

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

Add '21' to each side of the equation.
-21 + 21 + -4h = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -4h = 0 + 21
-4h = 0 + 21

Combine like terms: 0 + 21 = 21
-4h = 21

Divide each side by '-4'.
h = -5.25

Simplifying
h = -5.25
Subproblem 2
Set the factor '(4 + -1h)' equal to zero and attempt to solve:

Simplifying
4 + -1h = 0

Solving
4 + -1h = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1h = 0 + -4

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

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

Divide each side by '-1'.
h = 4

Simplifying
h = 4
Solution
h = {-5.25, 4}