3h^2+h^2=24h^3

Solution for 3h^2+h^2=24h^3 equation:

Simplifying
3h2 + h2 = 24h3

Combine like terms: 3h2 + h2 = 4h2
4h2 = 24h3

Solving
4h2 = 24h3

Solving for variable 'h'.

Combine like terms: 24h3 + -24h3 = 0
4h2 + -24h3 = 0

Factor out the Greatest Common Factor (GCF), '4h2'.
4h2(1 + -6h) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'h2' equal to zero and attempt to solve:

Simplifying
h2 = 0

Solving
h2 = 0

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

Simplifying
h2 = 0

Take the square root of each side:
h = {0}
Subproblem 2
Set the factor '(1 + -6h)' equal to zero and attempt to solve:

Simplifying
1 + -6h = 0

Solving
1 + -6h = 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 + -6h = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6h = 0 + -1
-6h = 0 + -1

Combine like terms: 0 + -1 = -1
-6h = -1

Divide each side by '-6'.
h = 0.1666666667

Simplifying
h = 0.1666666667
Solution
h = {0, 0.1666666667}