4h(3h+2)=h+12

Solution for 4h(3h+2)=h+12 equation:

Simplifying
4h(3h + 2) = h + 12

Reorder the terms:
4h(2 + 3h) = h + 12
(2 * 4h + 3h * 4h) = h + 12
(8h + 12h2) = h + 12

Reorder the terms:
8h + 12h2 = 12 + h

Solving
8h + 12h2 = 12 + h

Solving for variable 'h'.

Reorder the terms:
-12 + 8h + -1h + 12h2 = 12 + h + -12 + -1h

Combine like terms: 8h + -1h = 7h
-12 + 7h + 12h2 = 12 + h + -12 + -1h

Reorder the terms:
-12 + 7h + 12h2 = 12 + -12 + h + -1h

Combine like terms: 12 + -12 = 0
-12 + 7h + 12h2 = 0 + h + -1h
-12 + 7h + 12h2 = h + -1h

Combine like terms: h + -1h = 0
-12 + 7h + 12h2 = 0

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

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

Simplifying
-4 + -3h = 0

Solving
-4 + -3h = 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 + -3h = 0 + 4

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

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

Divide each side by '-3'.
h = -1.333333333

Simplifying
h = -1.333333333
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 = {-1.333333333, 0.75}