(2h+1)*h=91

Solution for (2h+1)*h=91 equation:

Simplifying
(2h + 1) * h = 91

Reorder the terms:
(1 + 2h) * h = 91

Reorder the terms for easier multiplication:
h(1 + 2h) = 91
(1 * h + 2h * h) = 91
(1h + 2h2) = 91

Solving
1h + 2h2 = 91

Solving for variable 'h'.

Reorder the terms:
-91 + 1h + 2h2 = 91 + -91

Combine like terms: 91 + -91 = 0
-91 + 1h + 2h2 = 0

Factor a trinomial.
(-7 + -1h)(13 + -2h) = 0

Subproblem 1
Set the factor '(-7 + -1h)' equal to zero and attempt to solve:

Simplifying
-7 + -1h = 0

Solving
-7 + -1h = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1h = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1h = 0 + 7
-1h = 0 + 7

Combine like terms: 0 + 7 = 7
-1h = 7

Divide each side by '-1'.
h = -7

Simplifying
h = -7
Subproblem 2
Set the factor '(13 + -2h)' equal to zero and attempt to solve:

Simplifying
13 + -2h = 0

Solving
13 + -2h = 0

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

Add '-13' to each side of the equation.
13 + -13 + -2h = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2h = 0 + -13
-2h = 0 + -13

Combine like terms: 0 + -13 = -13
-2h = -13

Divide each side by '-2'.
h = 6.5

Simplifying
h = 6.5
Solution
h = {-7, 6.5}