(4h+1)12h=36

Solution for (4h+1)12h=36 equation:

Simplifying
(4h + 1) * 12h = 36

Reorder the terms:
(1 + 4h) * 12h = 36

Reorder the terms for easier multiplication:
12h(1 + 4h) = 36
(1 * 12h + 4h * 12h) = 36
(12h + 48h2) = 36

Solving
12h + 48h2 = 36

Solving for variable 'h'.

Reorder the terms:
-36 + 12h + 48h2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + 12h + 48h2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-3 + h + 4h2) = 0

Factor a trinomial.
12((-1 + -1h)(3 + -4h)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(-1 + -1h)' equal to zero and attempt to solve:

Simplifying
-1 + -1h = 0

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

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

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

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

Simplifying
h = -1
Subproblem 2
Set the factor '(3 + -4h)' equal to zero and attempt to solve:

Simplifying
3 + -4h = 0

Solving
3 + -4h = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4h = 0 + -3

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

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

Divide each side by '-4'.
h = 0.75

Simplifying
h = 0.75
Solution
h = {-1, 0.75}