h(2h+5)=52

Solution for h(2h+5)=52 equation:

Simplifying
h(2h + 5) = 52

Reorder the terms:
h(5 + 2h) = 52
(5 * h + 2h * h) = 52
(5h + 2h2) = 52

Solving
5h + 2h2 = 52

Solving for variable 'h'.

Reorder the terms:
-52 + 5h + 2h2 = 52 + -52

Combine like terms: 52 + -52 = 0
-52 + 5h + 2h2 = 0

Factor a trinomial.
(-13 + -2h)(4 + -1h) = 0

Subproblem 1
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
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 = {-6.5, 4}