45h^2-6=3h

Solution for 45h^2-6=3h equation:

Simplifying
45h2 + -6 = 3h

Reorder the terms:
-6 + 45h2 = 3h

Solving
-6 + 45h2 = 3h

Solving for variable 'h'.

Reorder the terms:
-6 + -3h + 45h2 = 3h + -3h

Combine like terms: 3h + -3h = 0
-6 + -3h + 45h2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -1h + 15h2) = 0

Factor a trinomial.
3((-1 + -3h)(2 + -5h)) = 0

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

Simplifying
-1 + -3h = 0

Solving
-1 + -3h = 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 + -3h = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3h = 0 + 1
-3h = 0 + 1

Combine like terms: 0 + 1 = 1
-3h = 1

Divide each side by '-3'.
h = -0.3333333333

Simplifying
h = -0.3333333333
Subproblem 2
Set the factor '(2 + -5h)' equal to zero and attempt to solve:

Simplifying
2 + -5h = 0

Solving
2 + -5h = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5h = 0 + -2

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

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

Divide each side by '-5'.
h = 0.4

Simplifying
h = 0.4
Solution
h = {-0.3333333333, 0.4}