6h^2+9h-42=0

Solution for 6h^2+9h-42=0 equation:

Simplifying
6h2 + 9h + -42 = 0

Reorder the terms:
-42 + 9h + 6h2 = 0

Solving
-42 + 9h + 6h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + 3h + 2h2) = 0

Factor a trinomial.
3((-7 + -2h)(2 + -1h)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-7 + -2h)' equal to zero and attempt to solve:

Simplifying
-7 + -2h = 0

Solving
-7 + -2h = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2h = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2h = 0 + 7
-2h = 0 + 7

Combine like terms: 0 + 7 = 7
-2h = 7

Divide each side by '-2'.
h = -3.5

Simplifying
h = -3.5
Subproblem 2
Set the factor '(2 + -1h)' equal to zero and attempt to solve:

Simplifying
2 + -1h = 0

Solving
2 + -1h = 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 + -1h = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1h = 0 + -2
-1h = 0 + -2

Combine like terms: 0 + -2 = -2
-1h = -2

Divide each side by '-1'.
h = 2

Simplifying
h = 2
Solution
h = {-3.5, 2}